Exam 3 Review PDF

1703 EXAM 3 REVIEW 1. Know the symbols 2. Properties of z-distribution 3. Properties of t-distribution 4. Know the Central Limit Theorem 5. Know the properties of the binomial, normal, z and t distributions 6. Know the properties of confidence intervals 7. Find and interpret confidence inte...

1703 EXAM 3 REVIEW 1. Know the symbols 2. Properties of z-distribution 3. Properties of t-distribution 4. Know the Central Limit Theorem 5. Know the properties of the binomial, normal, z and t distributions 6. Know the properties of confidence intervals 7. Find and interpret confidence intervals 8. Assess claims using confidence intervals 9. Find the point estimate and margin of error given a confidence interval 10. Find the necessary sample size required to meet certain criteria 11. Be able to address any assumptions needed and assess their implications 12. Hypothesis testing (a) How to find hypotheses and what can go in them (b) Know assumptions to check (assess the distribution of 𝑋̅ and 𝑝̂ ) and why we care about them (c) Know what failure of assumptions means (d) Be able to use both the rejection region and p-value methods (e) Know what a p-value is (define it) (f) Define Type I error, Type II error, and power (g) Know decisions and conclusion statements (h) Know significance level (how would you choose one?), power, Type I and II errors Formulas Mean: ∑𝑥 ∑𝑥 OR 𝑛 𝑁 Standard Deviation: ∑(𝑥−𝑥̅ )2 ∑(𝑥−µ)2 √ OR √ 𝑛−1 𝑁 Standard deviation of 𝑥̅ : 𝜎 √𝑛 Standard deviation of p̂: 𝑝(1 − 𝑝) √ 𝑛 Confidence Intervals: ̂ (1− p p ̂) 𝑝̂ ± (z*) √ 𝑛 𝑠 𝑥̅ ± (t*) √𝑛 Test Statistics: 𝑝̂ − 𝑝 √𝑝 (1 − 𝑝) 𝑛 𝑥̅ − µ 𝑠 / √𝑛 Sample Size Determination: p̂(1-p̂) (z*)2 n = E2 z* 𝜎 2 n = ( ) E 1. In each of the following scenarios, determine the parameter of interest and the null and alternative hypotheses. (a) When debating the State Appropriation for TWU, the following question is asked: "Are the majority of students at TWU from Texas?" (b) A consumer test agency wants to see the whether the mean lifetime of a brand of tires is less than 42,000 miles. The tire manufacturer advertises that the average lifetime is at least 42,000 miles. (c) The length of a certain lumber from a national home building store is supposed to be 8.5 feet. A builder wants to check whether the shipment of lumber she receives has a mean length different from 8.5 feet. 2. Decreasing the sample size, while holding the confidence level the same, will do what to the width of your confidence interval? A. make it bigger B. make it smaller C. it will stay the same D. cannot be determined from the given information 3. A 95% confidence interval for the mean reading achievement score for a population of third-grade students is (44, 54). Suppose you compute a 99% confidence interval using the same information. Which of the following statements is correct? A. The intervals have the same width. B. The 99% interval is shorter C. The 99% interval is longer. D. The answer can’t be determined from the information given. 4. Decide if the researcher made a correct decision, a type I error, or a type II error given the following situation. Chewing gum shows promise as a new way to lose weight, so a researcher does a study to see if the proportion of people who chew gum and lose weight is greater than 0.50. The researcher uses an alpha of 0.05. (a) The researcher fails to reject the null hypothesis, when in fact the proportion of people who chew gum and lose weight is less than 0.50. (b) The researcher rejects the null hypothesis, when in fact the proportion of people who chew gum and lose weight is less than 0.50. (c) The researcher fails to reject the null hypothesis, when in fact the proportion of people who chew gum and lose weight is greater than 0.50. (d) The researcher rejects the null hypothesis, when in fact the proportion of people who chew gum and lose weight is greater than 0.50. 5. Are following are properties of the z-distribution, the t- distribution, both or neither. Standard deviation is greater than 1 Has a mean of zero Standard deviation is equal to 1 Is a normal distribution Also called standard normal distribution Area under the curve = 1 Has an infinite number of distributions Mean= median= mode 6. For the confidence interval (12, 25), find the point estimate and the margin of error. 7. A simple random sample of size n=45 is obtained from a population of student heights that is skewed with a mean of 65 inches and a standard deviation of 5 inches. Is the sampling distribution normally distributed? Why? A. Yes, the sampling distribution is normally distributed because the sample size is large enough and that’s all that matters. B. Yes, the sampling distribution is normally distributed because the sample size is large enough, but we should be cautious of the skewness. C. No, the sampling distribution is not normally distributed because the population is not normally distributed and the sample size is not large enough. D. No, the sampling distribution is not normally distributed because the population mean is less than 30. 8. The critical value for a 90% confidence interval for a one sample mean with a sample size of 27 is 9. The critical value for a 90% confidence interval for a one sample proportion with a sample size of 17 is 10. You want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of t* you would use for this interval is 11. We are 95% confident that the true population mean weight of all hockey players is between 192.51 pounds and 207.89 pounds. (a) Can we conclude the population mean weight is at least 190 pounds? (b) Can we conclude the population mean weight no more than 207 pounds? 12. True or False: (a) A 95% confidence interval implies that 95% of the data lies within the interval. (b) A 95% confidence interval implies that there is a 95% probability of capturing the parameter of interest within our interval. (c) A 95% confidence interval implies that with repeated sampling, 95% of the intervals constructed would contain the parameter of interest. 13. A random sample of 100 students at a university finds that these students take a mean of 15.3 credit hours per quarter with a standard deviation of 1.6 credit hours. Estimate the mean credit hours taken by a student each quarter using a 95% confidence interval. 14. Referring to a previous question (see #1): When debating the State Appropriation for TWU, the following question is asked: "Are the majority of students at TWU from Texas?" (a) At a significance level of.01, what is the critical value? (b) Given a test statistic of 2.504, state your decision. We can/cannot conclude that the majority of all TWU students are from the state of Texas. (c) What assumptions should be checked for this one-sample proportion? 15. The results of hypothesis test yield a p-value less the significance level, but it is discovered that the assumptions have not been met completely. Can the researcher conclude in favor of the Alternative Hypothesis? What type of error may have occurred? 16. Statistical Power 95% implies: 17. Significance level 0.05 implies: 18. Suppose you have the following hypothesis: 𝐻0 : 𝐹𝑟𝑎𝑛𝑘 ′ 𝑠 𝑟𝑜𝑐𝑘 − 𝑐𝑙𝑖𝑚𝑏𝑖𝑛𝑔 𝑒𝑞𝑢𝑖𝑝𝑡𝑚𝑒𝑛𝑡 𝑖𝑠 𝑠𝑎𝑓𝑒 𝐻1 𝐹𝑟𝑎𝑛𝑘 ′ 𝑠 𝑟𝑜𝑐𝑘 − 𝑐𝑙𝑖𝑚𝑏𝑖𝑛𝑔 𝑒𝑞𝑢𝑖𝑝𝑡𝑚𝑒𝑛𝑡 𝑖𝑠 𝑛𝑜𝑡 𝑠𝑎𝑓𝑒 (a) Which error is more severe? Type I or Type II. (b) The researcher should assess this information ahead of time to set an appropriate significance level. Which significance would you set if you were the researcher? a. 0.01 b. 0.05 c. 0.10 19. 35 married men are asked to report the number of times per week they help with household chores. The men report helping with household chores an average of 6.3 times per week with a standard deviation of 3.5 times. Is there significant evidence to conclude that all married men help with household chores less than 7 times per week? Use a significance level of 0.10. a. State the hypotheses. b. Check the assumptions. c. Determine the test statistic. d. Find the p-value and critical value. e. Make a decision. f. State the conclusion. 20. The drug Lipitor is meant to reduce total cholesterol and LDL cholesterol. In clinical trials, 19 out of 863 patients taking 10 mg of Lipitor daily complained of flu-like symptoms. Suppose that it is known that 1.9% of patients taking competing drugs complain of flu-like symptoms. Is there evidence to conclude that more than 1.9% of Lipitor users experience flu-like symptoms as a side effect at the α = 0.01 level of significance? a. State the hypotheses. b. Check the assumptions. c. Determine the test statistic. d. Find the p-value and critical value. e. Make a decision. f. State the conclusion.