PSY201 Final Exam Practice Questions PDF

Lecture 5 (Sampling Distribution) +-----------------------------------------------------------------------+ | 1. Suppose you're interested in the mean of a particular population | | of 100 total items. You take samples of 4 items per sample and | | calculate sample means ( x bar ) in the h...

Lecture 5 (Sampling Distribution) +-----------------------------------------------------------------------+ | 1. Suppose you're interested in the mean of a particular population | | of 100 total items. You take samples of 4 items per sample and | | calculate sample means ( x bar ) in the hopes of learning something | | about the population mean. After taking five samples of four items | | per sample, you notice that your value for  varies from sample to sample. How could the | | sampling distribution help you in this case? | | | | I. The sampling distribution would help you determine the typical | | value you should expect for x bar calculated for any sample of | | four taken from the population. | | | | II. The sampling distribution would show the variability of  values calculated from samples of four | | taken from the population. | | | |   a.  I only | | --- ----- ------------------ | |   b.  Both I and II | |   c.  Neither I nor II | |   d.  II only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 2. Which of the following are characteristics of sampling | | variability? | | | |   a.  Does not vary with sample size | | --- ----- --------------------------------------------------------- | | ------------------------------------------------------ | |   b.  Is constant from sample to sample | |   c.  Describes the difference between the observed value of a | | statistic and the corresponding population parameter | |   d.  Describes the sample-to-sample variability of a statistic | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 3. Based on historical records, the proportion of passengers on | | transatlantic cruises who request an inside cabin near the center of | | the ship is 28%. What can we say about the proportion of passengers | | taken from a sample of transatlantic cruises held during the months | | of January and February who request an inside cabin? | | | |   a.  Proportion for January-February cruises will be \< 28% | | --- ----- -------------------------------------------------------- | |   b.  Proportion for January-February cruises will be = 28% | |   c.  Proportion for January-February cruises will be \> 28% | |   d.  Cannot tell from the information given | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 4. Suppose you want to know the proportion of the residents of a | | metropolitan area (p) who use public transportation exclusively. You | | conduct four surveys of 1,500 people each and get the following | | sample proportions: . | | | | Using the four sample proportions above, what can we infer regarding | | the proportion of the metropolitan area residents (p) who use public | | transportation exclusively? | | | | I. The population proportion is equal to the average of the four | | sample proportions | | | | II. The population proportion lies somewhere between  and p\_4 hat | | | |   a.  I only | | --- ----- ------------------ | |   b.  Both I and II | |   c.  II only | |   d.  Neither I nor II | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 5. You're a market researcher for a company that manufactures winter | | outerwear. You would like to learn the proportion of mass transit | | riders in a particular region who need winter coats that are both | | waterproof and insulating. You plan to conduct 15 surveys of | | year-round transit riders in your area and use the surveys to | | construct a sampling distribution. You will be basing the upcoming | | year's manufacturing plans on the survey data, so you would like to | | minimize the standard deviation of the sampling distribution. Which | | of the following survey sizes (*n =* number of persons per survey) | | should you choose? | | | |   a.  n=20 | | --- ----- ------- | |   b.  n=8 | |   c.  n=50 | |   d.  n=150 | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 6. As the sample size increases, which of the following is true | | regarding the sampling distribution of ? | | | |   a.  The sampling distribution becomes more spread out | | --- ----- --------------------------------------------------------- | | ----------------------------- | |   b.  The sampling distribution becomes less spread out | |   c.  The sampling distribution is not affected by changes in s | | ample size | |   d.  The sampling distribution will become less spread out, bu | | t only if p is close to 0.5 | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 7. For which of the following would you expect the sampling | | distribution for p hat to be the least spread out and more tightly | | clustered about the population proportion p? | | | |   a.  I only | | --- ----- ---------- | |   b.  I and II | |   c.  I and IV | |   d.  II only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 8. A random sample is to be selected from a population that has a | | proportion of success p = 0.50. Determine the mean and standard | | deviation of the sampling distribution  for | | the sample size n = 100. | | | |   a.  Mean ( mu\_(p hat)) = 0.50; standard deviation  | | --- ----- --------------------------------------------------------- | | --------------------------------------- | |   b.  Mean ( mu\_(p hat)) = 0.85; standard deviation  | |   c.  Mean ( mu\_(p hat)) = 0.50; standard deviation  | |   d.  Mean ( mu\_(p hat)) = 0.50; standard deviation  | +-----------------------------------------------------------------------+ -- -- +-----------------------------------------------------------------------+ | 9. Suppose that a particular candidate for public office is favored | | by 33.0% of all registered voters in a district. If a polling | | organization took random samples of 60 voters, what would be the | | standard deviation (sigma\_(p hat)) and mean  of the sampling distribution of p hat (the | | per-sample proportion of voters favoring the candidate)? | | | |   a.  Standard deviation = 0.061, mean = 67.0% | | --- ----- ------------------------------------------ | |   b.  Standard deviation = 0.061, mean = 33.0% | |   c.  Standard deviation = 0.106, mean = 67.0% | |   d.  Standard deviation = 0.272, mean = 33.0% | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 10. Suppose the proportion of sunny days in a beachside tourist area | | is known to be 0.550. You survey groups of 12 tourists per group who | | visit the area regarding the proportion of their stay which was | | sunny. What is the standard deviation  and mean (mu\_(p hat)) of the sampling | | distribution of  (the proportion of sunny | | days during each tourist group's visit)? | | | |   a.  Standard deviation = 0.214, mean = 0.550 | | --- ----- ------------------------------------------ | |   b.  Standard deviation = 0.021, mean = 0.450 | |   c.  Standard deviation = 0.144, mean = 0.550 | |   d.  Standard deviation = 0.194, mean = 0.450 | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 11. You're researching the proportion of homes that sell within one | | month of being offered for sale. The housing market in the area | | you're researching has more home buyers than sellers, so the | | population proportion is 0.85. If you used a sample size of 20, would | | the sampling distribution of p hat have an approximately normal | | distribution? | | | |   a.  Yes, the sampling distribution of  would be approximately normal. | | --- ----- --------------------------------------------------------- | | ----------------------------------------------- | |   b.  No, the sampling distribution of p hat would not be appro | | ximately normal. | |   c.  The extent to which a sampling distribution can be approx | | imated as normal is unrelated to *n* and *p*. | |   d.  Cannot tell from the information given. | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 12. Suppose that the actual proportion of people at a particular | | company who use their bicycles to travel to work is 0.35. In a study | | of bicycle parking needs, the company's administration would like to | | estimate this proportion. They plan to take a random sample of 50 | | employees and use the sample proportion who use bicycles, , as an estimate of the population proportion. | | Estimate the standard deviation of the sample distribution. Suppose | | that another sample of different size has been selected and the | | standard deviation of this new sample distribution sigma\_(p hat) = | | 0.13. Would you expect more or less sample-to-sample variability in | | the sample proportions than for when *n *= 50? Is the sample size | | that resulted in  = 0.13 larger | | or smaller than 50? | | | |   a.  The standard deviation for the initial sample of the size | | *n* = 50 is 0.067. A standard deviation of 0.13 is greater than a st | | andard of 0.067, indicating lower sample-to-sample variability. The n | | ew sample size is smaller. | | --- ----- --------------------------------------------------------- | | --------------------------------------------------------------------- | | --------------------------------------------------------------------- | | ----------------------------- | |   b.  The standard deviation for the initial sample of the size | | *n* = 50 is 0.67. A standard deviation of 0.13 is less than a standa | | rd of 0.67, indicating lower sample-to-sample variability. The new sa | | mple size is larger. | |   c.  The standard deviation for the initial sample of the size | | *n* = 50 is 0.067. A standard deviation of 0.13 is greater than a st | | andard of 0.067, indicating higher sample-to-sample variability. The | | new sample size is smaller. | |   d.  The standard deviation for the initial sample of the size | | *n* = 50 is 0.067. A standard deviation of 0.13 is greater than a st | | andard of 0.067, indicating lower sample-to-sample variability. The n | | ew sample size is larger. | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 13. Suppose you have a population with proportion *p* = 0.88. How | | does the standard deviation of the sampling distribution p hat change | | for a sample size of *n* = 20 vs. a sample size of *n* = 100? For | | which is the sampling distribution approximately normal? | | | |   a.  For *n* = 20,  = 0.07 | | 27; for *n* = 100, sigma\_(p hat) = 0.0325; the sampling distribution | | is approximately normal for *n* = 100, but not for *n* = 20 | | --- ----- --------------------------------------------------------- | | --------------------------------------------------------------------- | | ------------------------------------------------------------------ | |   b.  For *n* = 20,  = 0.20 | | 98; for *n* = 100, sigma\_(p hat) = 0.0325; the sampling distribution | | is approximately normal for both *n* = 100 and for *n* = 20 | |   c.  For *n* = 20,  = 0.07 | | 27; for *n* = 100, sigma\_(p hat) = 0.0938; the sampling distribution | | is approximately normal for *n* = 100, but not for *n* = 20 | |   d.  For *n* = 20,  = 0.07 | | 75; for *n* = 100, sigma\_(p hat) = 0.1803; the sampling distribution | | is approximately normal for neither *n* = 100, nor for *n* = 20 | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 14. The spread of the sampling distribution of  decreases when: | | | |   a.  The population mean increases | | --- ----- --------------------------------------------- | |   b.  The sample size decreases | |   c.  The population standard deviation increases | |   d.  The sample size increase | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 15. What is the standard deviation of the sampling distribution of x | | bar for random samples of size 80 from a population with a mean of 48 | | and a standard deviation of 11? | | | |   a.  0.138 | | --- ----- ------- | |   b.  0.371 | |   c.  11 | |   d.  1.23 | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 16. According to the Central Limit Theorem, the distribution of which | | statistic can be approximately normal for any population | | distribution? What condition should the sample satisfy? | | | |   | | | |   a.  The Central Limit Theorem approximates the sample mean . It is applicable when the sample size *n* i | | s sufficiently large. | | --- ----- --------------------------------------------------------- | | --------------------------------------------------------------------- | | ----------------------- | |   b.  The Central Limit Theorem approximates the sample mean x | | bar. It is applicable when the sample size *n* is not large. | |   c.  The Central Limit Theorem approximates the sample size *n | | *. It is applicable when the sample size *n* is sufficiently large. | |   d.  The Central Limit Theorem approximates the sample size *n | | *. It is applicable when the sample size *n* is not large. | |   e.  The Central Limit Theorem approximates the population mea | | n *µ*. It is applicable when the sample size *n* is sufficiently larg | | e. | |   f.  The Central Limit Theorem approximates the population mea | | n *µ*. It is applicable when the sample size *n* is not large. | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 17. What is a sampling distribution of a statistic? | | | | ​ | | | |   a.  The distribution of the possible values of a statistic. | | --- ----- --------------------------------------------------------- | | --------------- | |   b.  The probability distribution of a random sample. | |   c.  The distribution of the possible values of a variable in | | a population. | |   d.  The average value of a population parameter. | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 18. Suppose we categorize populations as approximately normal or not, | | and samples as large or small. This categorization results in 4 | | categories: | | | | 1) Small samples from an approximately normal population | | ---- -------------------------------------------------------------- | | ---- | | 2) Large samples from an approximately normal population | | 3) Small samples from a population that is not approximately norm | | al | | 4) Large samples from a population that is not approximately norm | | al | | | | ​ | | | | What, if anything, can be said about the [shape] of the | | sampling distribution of  for each of these | | 4 situations? | | | | ​ | | | | +---------------------+---------------------+---------------------+ | | |   | a.  | 1) The sampling | | | | | | distribution of x | | | | | | bar will resemble | | | | | | the shape of the | | | | | | original population | | | | | | (not approximately | | | | | | normal). | | | | | | | | | | | | 2) The sampling | | | | | | distribution of  will | | | | | | be approximately | | | | | | normal. | | | | | | | | | | | | 3) The sampling | | | | | | distribution of x | | | | | | bar will be | | | | | | approximately | | | | | | normal.  | | | | | | | | | | | | 4) The sampling | | | | | | distribution of  will | | | | | | be approximately | | | | | | normal.  | | | +=====================+=====================+=====================+ | | |   | b.  | 1) The sampling | | | | | | distribution of x | | | | | | bar will be | | | | | | approximately | | | | | | normal. | | | | | | | | | | | | 2) The sampling | | | | | | distribution of  will | | | | | | resemble the shape | | | | | | of the original | | | | | | population (not | | | | | | approximately | | | | | | normal). | | | | | | | | | | | | 3) The sampling | | | | | | distribution of x | | | | | | bar will be | | | | | | approximately | | | | | | normal. | | | | | | | | | | | | 4) The sampling | | | | | | distribution of  will | | | | | | be approximately | | | | | | normal.  | | | +---------------------+---------------------+---------------------+ | | |   | c.  | 1) The sampling | | | | | | distribution of x | | | | | | bar will be | | | | | | approximately | | | | | | normal. | | | | | | | | | | | | 2) The sampling | | | | | | distribution of  will | | | | | | be approximately | | | | | | normal. | | | | | | | | | | | | 3) The sampling | | | | | | distribution of x | | | | | | bar will resemble | | | | | | the shape of the | | | | | | original population | | | | | | (not approximately | | | | | | normal). | | | | | | | | | | | | 4) The sampling | | | | | | distribution of  will | | | | | | be approximately | | | | | | normal.  | | | +---------------------+---------------------+---------------------+ | | |   | d.  | 1) The sampling | | | | | | distribution of x | | | | | | bar will be | | | | | | approximately | | | | | | normal. | | | | | | | | | | | | 2) The sampling | | | | | | distribution of  will | | | | | | be approximately | | | | | | normal. | | | | | | | | | | | | 3) The sampling | | | | | | distribution of x | | | | | | bar will be | | | | | | approximately | | | | | | normal.  | | | | | | | | | | | | 4) The sampling | | | | | | distribution of  will | | | | | | resemble the shape | | | | | | of the original | | | | | | population (not | | | | | | approximately | | | | | | normal). | | | +---------------------+---------------------+---------------------+ | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 19. Consider sampling from a skewed population. As the sample size, | | *n*, increases, some characteristics of the sampling distribution of | | x bar change. Does the increasing sample size cause changes in the | | characteristics of the sampling distribution? If so, specifically how | | does the mean of the sampling distribution of  change? | | | |   a.  As the sample size increases, mu\_(x bar) stays the same. | | --- ----- --------------------------------------------------------- | | --------------------------- | |   b.  As the sample size increases,  increases. | |   c.  As the sample size increases, mu\_(x bar) decreases. | |   d.  As the sample size increases,  becomes undefined. | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 20. Consider sampling from a skewed population. As the sample | | size, *n*, increases, some characteristics of the sampling | | distribution of x bar change. Does the increasing sample size cause | | changes in the characteristics of the sampling distribution? If so, | | specifically how does the standard deviation of the sampling | | distribution of  change? | | | |   a.  As the sample size increases, sigma\_(x bar) stays the sa | | me. | | --- ----- --------------------------------------------------------- | | ------------------------------ | |   b.  As the sample size increases,  increases. | |   c.  As the sample size increases, sigma\_(x bar) decreases. | |   d.  As the sample size increases,  becomes undefined. | +-----------------------------------------------------------------------+ Lecture 6 (Population estimate and confidence Interval) +-----------------------------------------------------------------------+ | 1. Which of the following properties of a statistic make it a good | | estimator of a population characteristic? | | | | I. It is unbiased (or nearly unbiased) | | | | II. It has a large standard error | | | |   a.  I only | | --- ----- ------------------ | |   b.  Neither I nor II | |   c.  II only | |   d.  Both I and II | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 2. Under which of the following conditions does the standard | | deviation sigma\_p hat of the sampling distribution of  become a good estimator of p? | | | | I. Under all conditions, because  is an unbiased estimator | | | | II. When the p is close to 0.5 | | | | III. When sampling size  is large | | | |   a.  Neither I nor II nor III | | --- ----- -------------------------- | |   b.  I only | |   c.  II only | |   d.  III only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 3. Three different statistics are being considered for estimating a | | population characteristic. The sampling distributions for all three | | statistics are shown below. | | | | Three separate graphs show Statistic I, Statistic II, and Statistic | | III. The Statistic I and Statistic II graphs are bell curves with a | | positive maximum and two zero minimums at the same horizontal | | distance from the maximum. In the Statistic I graph, the maximum is | | slightly to the right of the midpoint of the horizontal axis. In the | | Statistic II graph, the whole curve is to the left of the midpoint of | | the horizontal axis. The Statistic III graph curve rises from zero | | value at an increasing rate from the left end of the horizontal axis, | | then rises at a decreasing rate to the positive maximum slightly to | | the right of the midpoint of the horizontal axis, then decreases at | | an increasing rate to some positive value near the right end of the | | horizontal axis. | | | | Which statistic would you recommend using to estimate the population | | characteristics? | | | |   a.  Statistic I only | | --- ----- --------------------- | |   b.  Statistic II only | |   c.  Statistic III only | |   d.  Statistics I and II | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 4. An unbiased statistic is one that: | | | |   a.  Is closely approximated by a normal curve | | --- ----- --------------------------------------------------------- | | ---------------------------------------- | |   b.  Does not consistently tend to over- or underestimate the | | value of the population characteristic | |   c.  Is mound-shaped and has a small variance | |   d.  Is nearly symmetric | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 5. Under which of the following conditions does  the standard deviation of the sampling | | distribution of p hat decrease | | | | I.  decreases | | | | II. n increases | | | | III.  approaches 0.5 | | | |   a.  I only | | --- ----- ------------ | |   b.  II only | |   c.  I and III | |   d.  II and III | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 6. A random sample will be taken of all the students at a particular | | university. The sample proportion p hat will be used to estimate | | *p,* the proportion of all students who plan to graduate within the | | next 12 months. For which of the following situations will the | | estimate tend to be the closest to the actual value of *p*? | | | | I. *n* = 5800 and *p* = 0.5 | | | | II. *n* = 4800 and *p* = 0.4 | | | | III. *n* = 4800 and *p* = 0.2 | | | |   a.  I only | | --- ----- --------------------------------------------------------- | | --- | |   b.  II only | |   c.  III only | |   d.  I and III will be equally close to the actual value of *p | | * | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 7. Suppose you would like to use the sample proportion  to estimate the population proportion *p.* If | | your sample size is large, which of the following will also be true? | | | | I. You can approximate the sampling distribution of p hat by a | | normal distribution | | | | II. The standard deviation about the mean of the sampling | | distribution will be small | | | |   a.  I only | | --- ----- ------------------ | |   b.  Neither I nor II | |   c.  Both I and II | |   d.  II only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 8. For a given value of population proportion *p*, if the sample size | | *n* is increased by a factor of four, then which of the following | | best describes the resultant change in margin of error? | | | |   a.  Margin of error increases by a factor of two | | --- ----- ----------------------------------------------- | |   b.  Margin of error decreases by a factor of two | |   c.  Margin of error decreases by a factor of four | |   d.  Margin of error does not change | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 9. Suppose you have a population with a proportion of interest | |  If the sampling size n is large, which of the | | following is true regarding the likelihood that the proportion  of any given sample will differ from p by more | | than 1.96 times the standard error of p hat? | | | |   a.  It is likely that  will differ | | from  by more than 1.96 times the standard error of p hat | | --- ----- --------------------------------------------------------- | | --------------------------------------------------------------------- | | -------------- | |   b.  It is unlikely that  will diffe | | r from p by more than 1.96 times the standard error of  | |   c.  It is necessary to know the value of population proportio | | n p to answer this question. | |   d.  The likelihood that p hat will be with a given interval a | | round  is unrelated to the sample size n. | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 10. You're interested in the proportion of dog owners in your city | | who regularly make use of professional grooming services to care for | | their dog's coat. To estimate this population proportion p, you take | | a sample of 550 dog owners in your city and find that 88% of them | | make regular use of professional grooming services for their dogs' | | coats. What is the margin of error associated with using  to estimate p? (95% confidence level) | | | |   a.  Margin of error using p hat = 0.88 to estimate  is 0.033 | | --- ----- --------------------------------------------------------- | | ------------------------ | |   b.  Margin of error using p hat = 0.88 to estimate  is 0.078 | |   c.  Margin of error using p hat = 0.88 to estimate  is 0.014 | |   d.  Margin of error using p hat = 0.88 to estimate  is 0.027 | +-----------------------------------------------------------------------+ -- -- +-----------------------------------------------------------------------+ | 11. Which of the following are conditions for use of the margin of | | error formula when estimating a population proportion from a sample | | proportion? | | | | I) The sample is selected from a convenient portion of the population | | | | II) The sample is selected in a way that makes it reasonable to think | | that the sample is representative of the population | | | | III) For a given value of p hat, the products of  and n(1 minus p hat) are both less than or | | equal to 10 | | | |   a.  I only | | --- ----- ---------------- | |   b.  II only | |   c.  III only | |   d.  I and III only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 12. Which of the following should be true for the sampling method | | when using the margin of error formula to estimate a population | | proportion from a sample proportion? | | | | I. The sample is a random sample from the population of interest | | | | II. The sample is selected in a way that makes it reasonable to think | | that the sample is representative of the proportion of the | | population with the lowest values. | | | | III.  The sample is selected in a way that makes it reasonable to | | think that the sample is representative of the proportion of the | | population with the highest values. | | | |   a.  Neither I nor II nor III | | --- ----- -------------------------- | |   b.  I only | |   c.  II only | |   d.  III only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 13. A representative sample of 55 patients of a knee therapy clinic | | were surveyed regarding their adherence to a daily therapeutic | | exercise regimen. Based on the survey results, a proportion  = 0.52 reported adherence to a daily | | therapeutic exercise regimen. Which of the following could you use to | | express an estimate of the population proportion? (95% confidence | | level) | | | |   a.  Within 0.132 of 0.52 | | --- ----- --------------------------------------------------------- | | --------------------------------------------------------------------- | | --- | |   b.  Within 0.067 of 0.52 | |   c.  Within 0.132 of 0.48 | |   d.  Cannot calculate the margin of error since the sampling d | | istribution for p hat cannot be approximated by a normal distribution | |. | +-----------------------------------------------------------------------+ -- -- +-----------------------------------------------------------------------+ | 14. Which of the following affects the width of a confidence interval | | for a population proportion? | | | |   a.  Confidence level | | --- ----- ------------------------- | |   b.  Sample size | |   c.  Sample proportion value | |   d.  All of the these | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 15. Which of the following has the effect of reducing the confidence | | interval? | | | |   a.  Decreasing the sample size *n* | | --- ----- --------------------------------------------------------- | | --------------------- | |   b.  Increasing the sample size *n* | |   c.  For , increasing | | the value of p hat | |   d.  For , reducing t | | he value of p hat | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 16. Which of the following changes to the value of the sample | | proportion  reduce the confidence interval? | | | | I) For p hat less than 0.5, increasing the value of  | | | | II) For p hat less than 0.5, reducing the value of  | | | | III) For p hat less than 0.5, decreasing the value of  | | | | IV) For p hat less than 0.5, increasing the value of  | | | |   a.  I and II | | --- ----- ------------ | |   b.  III and IV | |   c.  I and III | |   d.  II and IV | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 17. A researcher has decided to decrease the confidence level in | | their estimation of a population proportion. What is the effect on | | the width of the associated confidence interval? | | | |   a.  The width of the confidence interval increases | | --- ----- --------------------------------------------------- | |   b.  The width of the confidence interval decreases | |   c.  The width of the confidence interval is unchanged | |   d.  There is not enough information to determine | +-----------------------------------------------------------------------+ -- -- +-----------------------------------------------------------------------+ | 18. Which of the following conditions must be met to use the | | large-sample confidence interval formula when estimating a population | | proportion? | | | | I. The sample is a random sample from the population of interest or | | selected in a way that makes it reasonable to think that the | | sample is representative of the population | | | | II. The sample is sufficiently large to include at least 10 successes | | and 10 failures | | | |   a.  I only | | --- ----- ------------------ | |   b.  II only | |   c.  Neither I nor II | |   d.  Both I and II | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 19. Suppose you want to use a large-sample 95% confidence interval to | | estimate the population proportion p using a random sample from the | | population of interest with proportion p hat = 0.65. Which of the | | following additional conditions must be met? | | | |   a.  The sample size  must be greater t | | han 100 | | --- ----- --------------------------------------------------------- | | ------------------------------ | |   b.  The product n p hat must be greater than or equal to 10 | |   c.  The product  must | | be equal to or less than 10 | |   d.  None of these | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 20. Suppose you want to estimate the population proportion p using a | | conveniently collected sample of interest with proportion  with a sample size n = 100. Can you | | use a large-sample 95% confidence interval? | | | |   a.  No, because the sampling method was not collected randoml | | y | | --- ----- --------------------------------------------------------- | | --------------- | |   b.  Yes, because  | |   c.  Yes, because n ( 1 minus p hat) greater than or equal to | | 10 | |   d.  Yes, because the sample size  is l | | arge | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 21. You're using the data from a survey of 500 randomly selected | | customers from your local coffee shop regarding the proportion who | | prefer coffee with cream for an afternoon beverage (p hat = 0.53). | | Part one: Would a large-sample confidence interval be an appropriate | | method for population proportion? Part Two: Would the large-sample | | confidence interval be appropriate if you wanted to know the relative | | proportions of customers who prefer coffee with cream, milk tea, and | | green tea? | | | |   a.  Part one: yes, because the survey was based on a random s | | ample sufficiently large to include at least 10 successes and 10 fail | | ures. Part two: yes, because it involves estimation from sampled data | |. | | --- ----- --------------------------------------------------------- | | --------------------------------------------------------------------- | | --------------------------------------------------------------------- | | ------------------------------------ | |   b.  Part one: no, because the survey was based on a sample in | | sufficiently large to include at least 10 successes and 10 failures. | | Part two: yes, because it involves estimation from categorical data. | |   c.  Part one: yes, because the survey was based on a random s | | ample sufficiently large to include at least 10 successes and 10 fail | | ures. Part two: yes, because it involves estimation from a single sam | | ple. | |   d.  Part one: yes, because the survey was based on a random s | | ample sufficiently large to include at least 10 successes and 10 fail | | ures. Part two: no, because it involves estimation from sampled data | | of multiple categorical variables. | +-----------------------------------------------------------------------+ -- -- +-----------------------------------------------------------------------+ | 22. Suppose that a random sample of 85 high school classrooms in the | | state of Iowa is selected and a 95% confidence interval for the | | proportion that has Internet access is (0.73, 0.79). Which of the | | following is a correct interpretation of the 95% confidence level? | | | |   a.  The method used to construct the interval will produce an | | interval that includes the value of the population proportion about | | 95% of the time in repeated sampling. | | --- ----- --------------------------------------------------------- | | --------------------------------------------------------------------- | | --------------------------------------- | |   b.  You can be 95% confident that the sample proportion is be | | tween 0.73 and 0.79. | |   c.  There is a 95% chance that the proportion of all high sch | | ool classrooms in Iowa that have Internet access is between 0.73 and | | 0.79. | |   d.  You can be 95% confident that the proportion of all high | | school classrooms in Iowa that have Internet access is between 0.73 a | | nd 0.79. | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 23. Suppose you have been asked to estimate the proportion of college | | students who have used smart phones to cheat on an exam. You have no | | prior knowledge of the population proportion , | | nor do you have any prior studies from which you could obtain a p | | hat. Your supervisor suggests that you include 151 students in the | | survey. If you assume a 95% confidence level, which of the following | | is an estimate of the margin of error under these conditions? | | | |   a.   | | --- ----- --------------------------------------------------- | |   b.  margin of error &lt;= 0.080 | |   c.   | |   d.  Cannot tell from the information given | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 24. You're planning a survey of students in your university to | | determine how many of them plan to study abroad for at least one | | academic term of their undergraduate program. What is the minimum | | number of students you should include in your survey if you want a | | margin of error no greater than 0.12 with a 90% confidence level? | | | |   a.  58 | | --- ----- ---- | |   b.  47 | |   c.  65 | |   d.  67 | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 25. Determine the confidence level associated with the given | | confidence interval using the standard normal curve. | | | |   | | | | The bell shaped curve is drawn in the coordinate plane, and the area | | below the curve and above the horizontal axis is separated into three | | parts, the central part is wider than the rest. The point separating | | the left and the central parts is marked on the horizontal axis at | | minus z subscript asterisk equals minus 1.96. The point separating | | the central and the right parts is marked on the horizontal axis as z | | subscript asterisk equals positive 1.96. The area of the left part is | | labeled as Lower-tail area equals 0.025. The area of the right part | | is labeled as Upper-tail area equals 0.025. The area of the central | | part is labeled as Central area equals 0.95. | | | |   | | | |   a.  95% | | --- ----- ------- | |   b.  0.05 | |   c.  5% | |   d.  0.025 | |   e.  1.96 | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 26. Which of the following factors affect the width of a confidence | | interval estimation of a population mean? | | | |   a.  Sample size | | --- ----- ----------------------------------- | |   b.  Population mean | |   c.  Sample mean for any single sample | |   d.  All of these | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 27. Suppose you're using a confidence interval to estimate a | | population mean. Which of the following are actions you can take to | | reduce the width of your confidence interval? | | | | I\) Decrease the sample size | | | | II\) Decrease the population standard deviation | | | | III\) Increase the sample size | | | | IV\) Decrease the confidence level | | | |   a.  II, III, and IV only | | --- ----- ---------------------- | |   b.  III and IV only | |   c.  I and II only | |   d.  III only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 28. Suppose you're planning to use a *t* critical value in | | calculating the confidence interval to estimate a population mean | | from a single-sample mean. Which of the following conditions must | | also be true? | | | | I. You must know the standard deviation of the population. | | | | II. Your sample must have been randomly selected or be representative | | of the population. | | | | III. Your sample size must be less than or equal to 30. | | | |   a.  I only | | --- ----- ------------------ | |   b.  II only | |   c.  III only | |   d.  I and II and III | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 29. Suppose you are estimating the mean number of visitors to an | | organic cherry farm on a typical summer. According to historical | | records, the number of summer visitors ranges from 100 to 300. If *n* | | = the number of years of historical records sampled, what is the | | minimum *n* needed to give a margin of error of 33 visitors or less? | | Assume 95% confidence. | | | |   a.  9 years | | --- ----- ---------- | |   b.  3 years | |   c.  21 years | |   d.  15 years | +-----------------------------------------------------------------------+ -- -- +-----------------------------------------------------------------------+ | 30. If you know that the population standard deviation of a | | particular population is 15 and the sample size is 36, what is the | | margin of error for estimating the population mean? Assume 95% | | confidence. | | | |   a.  4.9 | | --- ----- ----- | |   b.  2.5 | |   c.  0.8 | |   d.  9.6 | +-----------------------------------------------------------------------+ -- -- Lecture 7 (Hypothesis testing) +-----------------------------------------------------------------------+ | 1. Suppose you're conducting a hypothesis test. Your data does not | | provide convincing evidence that the null hypothesis is false. Which | | of the following can you conclude? | | | | I. You fail to reject the null hypothesis | | | | II. You reject the alternative hypothesis | | | | III. You support the hull hypothesis | | | |   a.  Neither I nor II nor III | | --- ----- -------------------------- | |   b.  I only | |   c.  II only | |   d.  III only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 2. In choosing between null and alternative hypotheses, which of the | | following is initially assumed? | | | |   a.  The alternative hypothesis is true | | --- ----- --------------------------------------------------------- | |   b.  The null hypothesis is true | |   c.  Neither the alternative nor the null hypothesis is true | |   d.  Both the alternative and the null hypotheses are true | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 3. If you have data that provides convincing evidence that the null | | hypothesis is false, then which of the following conclusions can you | | make in a hypothesis test? | | | | I. Reject the null hypothesis | | | | II. Support the null hypothesis | | | | III. Reject the alternative hypothesis | | | |   a.  Neither I nor II nor III | | --- ----- -------------------------- | |   b.  I only | |   c.  II only | |   d.  III only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 4. Suppose you're conducting a hypothesis test. The data you gather | | might or might not occur if the null hypothesis were true. Which of | | the following can you conclude? | | | | I. Fail to reject the null hypothesis because you did not have | | convincing evidence against it | | | | II. Fail to reject the null hypothesis because you have strong | | evidence that it was true | | | | III. Reject the null hypothesis because you had convincing evidence | | against it. | | | |   a.  Neither I nor II nor III | | --- ----- -------------------------- | |   b.  I only | |   c.  II only | |   d.  III only | +-----------------------------------------------------------------------+ -- -- +-----------------------------------------------------------------------+ | 5. A city bus scheduler is interested in whether the proportion of | | intercity express buses arriving at the central station exceeds 75%. | | They randomly sample the arrival timeliness of a sample of intercity | | buses and use the data as a basis for choosing between: *H*~0~ = | | 0.75, *H~a~* \> 0.75 which of the following describes a Type I error | | for this hypothesis test? | | | | I. It is concluded that more than 75% of intercity buses arrive on | | time when the actual proportion which arrives on time is equal to | | or less than 75%. | | | | II. It is concluded that 75% or fewer buses arrived on time when the | | actual proportion of on-time arrivals exceeded 75%. | | | |   a.  Neither I nor II | | --- ----- ------------------ | |   b.  I only | |   c.  Both I and II | |   d.  II only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 6. Which of the following are true regarding Type I and Type II | | errors associated with hypothesis testing? | | | |   a.  I only | | --- ----- ----------------- | |   b.  II only | |   c.  III only | |   d.  II and III only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 7. Assuming the same sample size is used, how does changing the | | significance level from 0.2 to 0.05 affect the probability of | | rejecting the null hypothesis when the alternative hypothesis is | | true? | | | |   a.  Probability decreases | | --- ----- --------------------------------------------------------- | | ------ | |   b.  Probability increases | |   c.  Probability does not change | |   d.  Probability changes, but it might either decrease or incr | | ease | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 8. Which of the following is an initial assumption in a hypothesis | | test? | | | |   a.  The null hypothesis is false | | --- ----- --------------------------------------------------------- | | ----------------- | |   b.  The proportion of the sample used to test the hypothesis | | is close to 0.5 | |   c.  The alternate hypothesis is true | |   d.  The null hypothesis is true | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 9. If a null hypothesis *p* = 0.65 is true, and we know the standard | | error of the sampling distribution for , | | and we know that the sampling distribution can be approximated as a | | normal distribution, which of the following can we also determine? | | | | I. The *z*-statistic for any known sample proportion p hat | | | | II. The probability of observing a z-value is at least as unusual as | | the *z*-statistic for  | | | | III. The chance of seeing a sample proportion p hat at a given | | distance from *p* = 0.65 | | | |   a.  I and II | | --- ----- ---------------- | |   b.  II and III | |   c.  I and III | |   d.  I, II, and III | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 10. Which of the following describes what a *z*-statistic measures in | | the context of hypothesis testing? | | | | I. The distance between the sample statistic  and the population proportion *p* | | | | II. The distance between the sample statistic p hat and the value | | predicted by the alternative hypothesis in terms of the standard | | error of  | | | | III. The distance between the sample statistic p hat and the null | | hypothesis value in terms of the standard error of  | | | |   a.  Neither I nor II nor III | | --- ----- -------------------------- | |   b.  I only | |   c.  II only | |   d.  III only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 11. Suppose you're conducting a hypothesis test with a null | | hypothesis *p* = 0.35. If you calculate a *z*-statistic of 4.00 for a | | particular sample proportion p hat, then which of the following is | | true? | | | | I. The sample proportion  was 4.00 | | standard errors below the 0.35. | | | | II. The sample proportion p hat was 4.00 standard errors above 0.35 | | | | III. The sample proportion  was within | | 4.00 standard errors of 0.35 | | | |   a.  Neither I nor II nor III | | --- ----- -------------------------- | |   b.  I only | |   c.  II only | |   d.  III only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 12. Suppose you're conducting a hypothesis test with *H*~0 ~= 0.68, | | *H*~a ~\> 0.68, *α* = 0.15. You take a random sample with *n* = 200 | | and get a p hat= 0.72. Which of the following can we say regarding | | the null hypothesis? | | | |   a.  *P* - value = 0.113, reject the null hypothesis since *P* | | - value \< *α* | | --- ----- --------------------------------------------------------- | | -------------------------- | |   b.  *P* - value = 0.887, fail to reject the null hypothesis s | | ince *P* - value \> *α* | |   c.  *P* - value = 0.389, reject the null hypothesis since *P* | | - value \> *α* | |   d.  *P* - value = 0.611 , fail to reject the null hypothesis | | since *P* - value \> *α* | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 13. Suppose you're conducting a hypothesis test with *H*~0 ~= 0.38, | | *H*~a ~\> 0.38, *α* = 0.05. You take a random sample and use the n | | and from that sample to determine a | | P-value of 0.12. Which of the following can we say regarding the null | | hypothesis? | | | | I. Reject the null hypothesis since the *P* - value  is greater than | | the *α *- value | | | | II. Fail to reject the null hypothesis since the *P* - value  is | | greater than the *α *- value | | | | III. Reject the alternative hypothesis since *P* - value  is greater | | than the *α* - value | | | |   a.  Neither I nor II nor III | | --- ----- -------------------------- | |   b.  I only | |   c.  II only | |   d.  III only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 14. Suppose you're conducting a hypothesis test with *H*~0 ~= 0.38, | | *Ha*~ ~\> 0.38, *α* = 0.15. You take a random sample and use the n | | and p hatfrom that sample to determine a P-value of 0.15. Which of | | the following can we say regarding the null hypothesis? | | | | I. Reject the null hypothesis since the *P* - value is not greater | | than the *α *- valuee | | | | II. Fail to reject the null hypothesis since the *P* - value is | | greater than or equal to the *α *- value | | | | III. Reject the null hypothesis since *P* - value is greater than or | | equal to the *α* - value | | | |   a.  Neither I nor II nor III | | --- ----- -------------------------- | |   b.  I only | |   c.  II only | |   d.  III only | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 15. Assuming a random sample from a large population, for which of | | the following null hypotheses and sample sizes is the large-sample | | *z* test appropriate? | | | |   a.  *H*~0~: *p*~0 ~= 0.10, *n* = 75 | | --- ----- --------------------------------- | |   b.  *H*~0~: *p*~0~ = 0.15, *n* = 50 | |   c.  *H*~0~: *p*~0 ~= 0.6, *n* =200 | |   d.  *H*~0~: *p*~0 ~= 0.3, *n* =20 | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 16. Assuming a random sample from a large population, for which of | | the following null hypotheses and sample sizes would the large-sample | | *z* test [not] be appropriate? | | | |   a.  *H*~0~: *p*~0 ~= 0.9, *n* = 200 | | --- ----- ---------------------------------- | |   b.  *H*~0~: *p*~0~ = 0.10, *n* = 150 | |   c.  *H*~0~: *p*~0 ~= 0.08, *n* = 100 | |   d.  *H*~0~: *p*~0 ~= 0.8, *n* = 100 | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 17. Suppose residents of a particular neighborhood are concerned | | about the arsenic level in their tap water. Health authorities have | | established that arsenic levels in tap water should be kept below 10 | | parts per million (ppm). Which of the following hypothesis could the | | residents test in order to determine if their drinking water has | | unsafe levels of arsenic? Let µ represent the arsenic levels of the | | neighborhood tap water. | | | |   a.   | | --- ----- --------------------------------------------------------- | | ---------------------- | |   b.  H\_0 : mu = 10 ppm versus H\_a : mu != 10 ppm | |   c.   | |   d.  H\_0 : mu less than 10 ppm versus H\_a : mu greater than | | 10 ppm | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 18. Suppose residents of a mountain town are concerned about the | | level of airborne particulates from wood stoves on the local air | | quality. Health authorities have established maximum levels of 15 | | micrograms per cubic meter for smoke particulates. Which of the | | following hypothesis could the residents test in order to determine | | if their air quality was unhealthy? Let µ represent the smoke | | particulate levels in micrograms per cubic meter in the local air. | | | |   a.   | | --- ----- --------------------------------------------------------- | | ------------ | |   b.  H\_0 : mu = 15 versus H\_a : mu != 15 | |   c.   | |   d.  H\_0 : mu = 15 versus H\_a : mu greater than 15 | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 19. The local airport authority wants to investigate whether the mean | | of handled passengers per month has increased from 64,500 to plan | | maintenance works. Determine the valid null and alternative | | hypotheses. | | | |   | | | |   a.  *H*~0~:  \> 64,500 versus *Ha*: | | x bar  = 64,500 | | --- ----- --------------------------------------------------------- | | ------------------ | |   b.  *H*~0~: *µ* = 64,500 versus *Ha*: *µ* \> 64,500 | |   c.  *H*~0~:  = 64,500 versus *Ha*: | | *µ* \> 64,500 | |   d.  *H*~0~: *µ* \> 64,500 versus *Ha*: *µ* = 64,500 | |   e.  *H*~0~: x bar = 64,500 versus *Ha*:  \> 64,500 | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | 20. Determine the *P*-value in a hypothesis test for a population | | mean with *H*~0~: *µ* = hypothesized value and *Ha*: *µ* | | \> hypothesized value. | | | |   | | | |   a.  area to the right of the calculated *t* under the *t* cur | | ve with df = *n* − 2 | | --- ----- --------------------------------------------------------- | | ---------------------- | |   b.  area to the left of the calculated *t* under the *t* curv | | e with df = *n* − 1 | |   c.  area to the right of the calculated *t* under the *t* cur | | ve with df = *n* − 1 | |   d.  area to the left of the calculated *t* under the *t* curv | | e with df = *n* − 2 | |   e.  area to the right of the calculated *t* under the *t* cur | | ve with df = *n* | +-----------------------------------------------------------------------+ Lecture 8 (two-sample and paired-sample t tests) +-----------------------------------------------------------------------+ | 1. Suppose you are interested in the proportion of two populations. | | You gather a random sample from each population. What else must you | | do if you would like to use a large sample confidence interval to | | express the difference in the population proportions? | | | | I. Ensure that the sample size you us