Final Exam Study Guide PDF

1) Find the critical value of t for a two-tailed test with 12 degrees of freedom using 𝛼 = 0.05. a. 1.782 b. 1.796 c. 2.179 d. 2.201 2) If the null hypothesis is rejected in hypothesis testing, a. no conclusions can be drawn from the test. b. the data must have been accumulated incorrectl...

1) Find the critical value of t for a two-tailed test with 12 degrees of freedom using 𝛼 = 0.05. a. 1.782 b. 1.796 c. 2.179 d. 2.201 2) If the null hypothesis is rejected in hypothesis testing, a. no conclusions can be drawn from the test. b. the data must have been accumulated incorrectly. c. the alternative hypothesis is true. d. the sample size has been too small. 3) When the following hypotheses are being tested at a level of significance of 𝛼, H0: 𝜇 ≥ 500 Ha: 𝜇 < 500 the null hypothesis will be rejected if a. p-value > 𝛼. b. p-value = 𝛼 2 c. p-value ≤ 𝛼. d. p-value ≤ 1 − 𝛼 /2 4) Which of the following does not need to be known in order to compute the p-value? a. knowledge of whether the test is one-tailed or two-tailed b. the value of the test statistic c. the level of significance d. the probability distribution of the test statistic 5) On September 21, 2022, the CDC announced that 40% of women in the United States were currently suffering from anxiety. Hoping that the proportion of women suffering from anxiety in her country was lower, Koko selected a random sample of 66 adult women from her country to find 23 of them suffering from anxiety. Does this provide evidence at the 8% level of significance of a lower proportion of women with anxiety in her county? Conduct the hypothesis test using a p-value approach. a) The hypotheses are H0: p ≥ 0.4 and Ha: p < 0.4. The test statistic is z = −0.85.The p-value = 0.1965. The conclusion is to not reject H0. We cannot conclude that the proportion of women in Koko's country suffering from anxiety is significantly less than 40%. b) The hypotheses are H0: p ≤ 0.4 and Ha: p > 0.4. The test statistic is z = 0.88. The p-value = 0.1899. The conclusion is to reject H0. We conclude that the proportion of women in Koko's country suffering from anxiety is significantly less than 40%. c) The hypotheses are H0: p ≤ 0.4 and Ha: p > 0.4. The test statistic is z = 0.85. The p-value = 0.1965. The conclusion is to reject H0. We conclude that the proportion of women in Koko's country suffering from anxiety is significantly less than 40%. d) The hypotheses are H0: p ≥ 0.4 and Ha: p < 0.4. The test statistic is z = −0.88. The p-value = 0.1899. The conclusion is to not reject H0. We cannot conclude that the proportion of women in Koko's country suffering from anxiety is significantly less than 40%. 6) In a two-tailed hypothesis test situation, the test statistic is determined to be t = −1.696. The sample size is 32. What is the p-value for this test? a) −0.1 b) −0.05 c) 0.05 d) 0.1 7) Alonte volunteers at a local animal shelter that works to keep the mean adoption time for animals to be at most four weeks. Alonte's friend Zana conducts a random sample of 22 animals from the shelter and finds the mean time for them to have been adopted was 4.822weeks with a standard deviation of 1.27 weeks. Assume the population of adoption times is approximately normal. Does this provide evidence at the 1% significance level of a longer mean time than wanted for the shelter? Conduct the hypothesis test using a p-value approach. a) The hypotheses are H0: 𝜇 ≤ 4 weeks and Ha: 𝜇 > 4 weeks. The test statistic is t= 3.036. The p-value = 0.0031. The conclusion is to reject H0. We conclude that the mean adoption time for the shelter is significantly greater than four weeks. b) The hypotheses are H0: 𝜇 ≤ 4 weeks and Ha: 𝜇 > 4 weeks. The test statistic is z = 3.036. The p-value = 0.0063. The conclusion is to reject H0. We conclude that the mean adoption time for the shelter is significantly greater than four weeks. c) The hypotheses are H0: 𝜇 ≥ 4 weeks and Ha: 𝜇 < 4 weeks. The test statistic is t = 3.036. The p-value = 0.0031. The conclusion is to fail to reject H0. We cannot conclude that the mean adoption time for the shelter is significantly greater than four weeks. d) The hypotheses are H0: 𝜇 ≥ 4 weeks and Ha: 𝜇 < 4 weeks. The test statistic is z = 3.036. The p-value = 0.0063. The conclusion is to fail to reject H0. We cannot conclude that the mean adoption time for the shelter is significantly greater than four weeks. 8) Read the z statistic from the normal distribution table and choose the correct answer. For a two-tailed test using 𝛼 = 0.0854, find the critical z value. a) 0.82 b) 1.375 c) 1.72 d) 2.85 9) Read the t statistic from the t distribution table and choose the correct answer. For a one- tailed test (lower tail), using a sample size of 11, and at the 1% level of significance, find the critical t value. a) −2.764 b) −2.718 c) 2.718 d) 2.764 10) A two-tailed test is performed at the 0.05 level of significance. The p-value is determined to be 0.04. The null hypothesis a) must be rejected. b) has been designed incorrectly. c) could be rejected, depending on the sample size. d) should not be rejected. 11) The average manufacturing work week in a particular city was 40.3 hours last year. It is believed that a recession has led to a reduction in the average work week. To test the validity of this belief, which is the correct hypotheses? a) H0: 𝜇 < 40.3 Ha: 𝜇 ≥ 40.3 b) H0: 𝜇 > 40.3 Ha: 𝜇 ≤ 40.3 c) H0: 𝜇 ≥ 40.3 Ha: 𝜇 < 40.3 d) H0: 𝜇 = 40.3 Ha: 𝜇 ≠ 40.3 12) The average monthly rent for one-bedroom apartments in a particular city has been $740. Because of a downturn in the real estate market, it is believed that there has been a decrease in the average rental. Which is the correct hypotheses to be tested? a) H0: 𝜇 = 740 Ha: 𝜇 ≠ 740 b) H0: 𝜇 > 740 Ha: 𝜇 ≤ 740 c) H0: 𝜇 ≥ 740 Ha: 𝜇 < 740 d) H0: 𝜇 < 740 Ha: 𝜇 ≥ 740 13) The average hourly wage of computer programmers with 2 years of experience has been $22.60. Because of high demand for computer programmers, it is believed there has been  a significant increase in the average hourly wage of computer programmers. To test if there has been an increase, which of the following are the correct hypotheses to be tested? a) H0: 𝜇 ≤ 22.60 Ha: 𝜇 > 22.60 b) H0: 𝜇 > 22.60 Ha: 𝜇 ≤ 22.60 c) H0: 𝜇 = 22.60 Ha: 𝜇 ≠ 22.60 d) H0: 𝜇 < 22.60 Ha: 𝜇 ≥ 22.60 14) A juice drink filling machine, when in perfect adjustment, fills the bottles with 14 ounces of drink on an average. Any overfilling or underfilling results in the shutdown and readjustment of the machine. Which of the following is the correct set of hypotheses to determine whether or not the machine is properly adjusted? a) H0: 𝜇 < 14 Ha: 𝜇 ≥ 14 b) H0: 𝜇 ≤ 14 Ha: 𝜇 > 14 c) H0: 𝜇 = 14 Ha: 𝜇 ≠ 14 d) H0: 𝜇 ≠ 14 Ha: 𝜇 = 14 15) The academic planner of a university thinks that at least 32% of the entire student body attends summer school. Which of the following is the correct set of hypotheses to test his belief? a) H0: p < 0.32 Ha: p ≥ 0.32 b) H0: p ≤ 0.32 Ha: p > 0.32 c) H0: p ≥ 0.32 Ha: p < 0.32 d) H0: p > 0.32 Ha: p ≤ 0.32 16) Given the following information, n = 36, x = 60, s = 12 H0: 𝜇 ≥ 51 Ha: 𝜇 < 51 what is the test statistic? a) −4.5 b) −0.22 c) 0.22 d) 4.5 17) A sample of 2,200 items had 440 defective items. For the hypothesis test H0: p ≤ 0.20 Ha: p > 0.20, what is the test statistic? a) 0 b) 0.20 c) 0.22 d) 0.44 18) A random sample of 100 people was taken. Eighty-four of the people in the sample favored Candidate A. We are interested in determining whether the proportion of the population in favor of Candidate A is significantly more than 80%. The test statistic is 1. Find the p-value. a) 0.02 b) 0.04 c) 0.1587 d) 0.3174 19) A grocery store has an average sales of $6,000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 100 days of sales was selected. It was found that the average was $6,350 per day. From past information, it is known that the standard deviation of the population is $1,500. Find the value of the test statistic. a) 0.023 b) 0.233 c) 2.33 d) 23.33 20) When the area corresponding to the critical value is in the lower tail of the sampling distribution, the p-value is the area under the curve a) less than or equal to the critical value. b) greater than or equal to the critical value. c) less than or equal to the test statistic. d) greater than or equal to the test statistic. 21) A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Five Today Years Ago x 84 89  𝜎2 112.5 54 n 45 36 Find the point estimate for the difference between the means of the two populations. (Use Today − Five Years Ago.) a) −9 b) −5 c) 9 d) 58.5 22) A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Five Today Years Ago x 80 89 𝜎2 225.5 136.5 n 41 39 The point estimate for the difference between the means is −9 and the standard error is 3. Find the test statistic for the difference between the two population means. (Use Today − Five Years Ago.) a) −3 b) −1.5 c) −0.65 d) −0.47 23) A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Five Today Years Ago  x 86 89 𝜎2 102.5 58.5 n 41 39 The test statistic is −1.5. Find the p-value for the difference between the two population means. (Use Today − Five Years Ago.) a) 0.0668 b) 0.1336 c) 0.8664 d) 0.9332 24) The following information was obtained from independent random samples taken of two populations. Assume normally distributed populations. Sample 1 Sample 2 Sample Mean 46 42 Sample Variance 120 169 Sample Size 10 13 The point estimate of the difference between the means is 4, the standard error is 5, and the degrees of freedom are 20. What is the 95% confidence interval for the difference between the two population means? (Use Sample 1 − Sample 2.) a) −6.43 to 14.43 b) −6 to 4 c) −1 to 9 d) 1.91 to 6.09 25) In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. Downtown North Mall Store Store Sample size 25 20 Sample mean $11 $7  Sample standard $3 $1 deviation The point estimate for the difference between the two population means is 4. Find a 95% interval estimate for the difference (in dollars) between the two population means. (Use Downtown Store − North Mall Store.) a) $0.65 to $2.62 b) $1.96 to $6.04 c) $2.69 to $5.31 d) $3.70 to $6.30 26) In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. Company A Company B Sample size 75 60 Sample mean $15.75 $15.25 Population standard deviation $1.00 $0.95 The point estimate for the difference between the two population means is $0.50. Find the test statistic. (Use Company A − Company B.) a) 0.17 b) 1.68 c) 2.97 d) 4.20 27) In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. Company A Company B Sample size 70 55 Sample mean $14.75 $14.35 Population standard deviation $1.00 $0.95 The test statistic is 2.28. Find the p-value. (Use Company A − Company B.) a) 0.0112 b) 0.0224  c) 0.0448 d) 0.9776 28) In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. Company A Company B Sample size 70 55 Sample mean $15.75 $15.25 Population standard deviation $1.00 $0.95 The p-value is 0.0044. At the 5% level of significance, the null hypothesis a) should not be tested. b) should be revised. c) should not be rejected. d) should be rejected. 29) The results of a recent poll on the preference of shoppers regarding two products are shown below. Shoppers Shoppers Favoring Product Surveyed This Product A 800 480 B 900 486 The point estimate for the difference between the two population proportions is 0.06 and the margin of error is 0.0470. Find the 95% confidence interval estimate for the difference between the population proportions favoring the products. (Use Product A − Product B.) a) 0.013 to 0.107 b) 0.013 to 0.6 c) 0.038 to 0.058 d) 0.5 to 0.6 30) Of the two production methods, a company wants to identify the method with the smaller population mean completion time. One sample of workers is selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on a) worker samples. b) pooled samples. c) matched samples. d) independent samples. 31) The sampling distribution of p1 − p2 is approximated by a normal distribution if _____ are all greater than or equal to 5. a) n1p2, p2(1 − n2), n2p1, p1(1 − n1) b) n1p1, p1(1 − n1), n2p2, p2(1 − n2) c) n1p1, n1(1 − p1), n2p2, n2(1 − p2) d) n1p2, n1(1 − p2), n2p1, n2(1 − p1) 32) In simple linear regression, r2 is the a) mean square error. b) correlation coefficient. c) coefficient of determination. d) squared residual. 33) In regression analysis, the model in the form y = 𝛽0 + 𝛽1x + 𝜀 is called the a) regression equation. b) correlation model. c) regression model. d) estimated regression equation. 34) The model developed from sample data that has the form of ŷ = b0 + b1x is known as the a) regression equation. b) correlation model. c) estimated regression equation. d) regression model. 35) In the following estimated regression equation ŷ = b0 + b1x, a) b1 is the intercept. b) b1x is the slope. c) b1 is the slope. d) b1x is the intercept. 36) The standard error of the estimate is the a) standard deviation of t. b) square root of SSE. c) square root of MSE. d) square root of SST. 37) In a regression analysis, the standard error of the estimate is determined to be 9. In this situation, the MSE a) is 3. b) depends on the sample size. c) is 81. d) requires a known SSE. 38) A regression analysis between sales (y in $1,000s) and advertising (x in dollars) resulted in the following equation. ŷ = 70,000 + 4x The above equation implies that a) an increase of $1 in advertising is associated with an increase of $4,000 in sales. b) an increase of $1 in advertising is associated with an increase of $73,000 in sales. c) an increase of $1 in advertising is associated with an increase of $4 in sales. d) an increase of $3 in advertising is associated with an increase of $4,000 in sales. 39) A regression analysis between sales (y in dollars) and advertising (x in dollars) resulted in the following equation: ŷ = 16,500 + 71.5x For a predicted sale of $67,980, what should be the advertising dollar amount? a) $705 b) $720 c) $820 d) $835 40) Which of the following is correct? a) SSE = SSR + SST b) SSR = SSE + SST c) SST = SSR + SSE d) SST = SSR – SSE 41) In a regression analysis, the correlation coefficient is 0.45. What is the coefficient of determination in this situation? a) 0.2025 b) 0.6708 c) 4.00 d) 21.16 42) In a regression analysis, if SSE = 100 and SSR = 800, find the coefficient of determination. a) 0.10 b) 0.13 c) 0.80 d) 0.89 43) Regression analysis was applied between demand for a product (y) and the price of the product (x), and the following estimated regression equation was obtained. ŷ = 130 − 20x  Based on the above estimated regression equation, if price is increased by 5 units, then demand is expected to a) increase by 100 units. b) decrease by 100 units. c) increase by 130 units. d) decrease by 20 units. 44) In a Linear Regression Model, the correlation coefficient was calculated to be −0.8660 and the SSE was 120. What would be SST for this Model? a) −420 b) 124.3087 c) 360 d) 480 45) If the correlation coefficient is a negative value, then the a) intercept of the regression line must also be positive. b) coefficient of determination can be either a negative or a positive value, depending on the slope. c) slope of the regression line must be negative. d) regression equation could have either a positive or a negative slope. 46) A random sample of 49 statistics examinations was taken. The average score, in the sample, was 82 with a variance of 12.96. What is the 95% confidence interval for the average examination score of the population of the examinations? a) 76.00 to 88.00 b) 78.40 to 85.60 c) 80.97 to 83.03 d) 81.15 to 82.85 47) The manager of a grocery store has taken a random sample of 225 customers. The average length of time it took these 225 customers to check out was 4 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. The standard error is 0.0667. At 95% confidence, what is the margin of error associated with the sample mean? a) 0.110 b) 0.131 c) 1.097 d) 1.307 48) Random samples of size 19 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 6. Find the mean and the standard deviation of the sampling distribution of the sample means. a) 6 and 1.38 b) 36 and 1.32 c) 36 and 1.38 d) 36 and 6 49) Lorenzo volunteers at a pet shelter that claims to have half of the animals adopted within two weeks of their arrival at the shelter. Suppose that there are 144 animals at the shelter on a given day and that it is known that half of these animals will be adopted within two weeks of their arrival. Lorenzo randomly selects 20 of the 144 animals. What is the probability that at least 13 animals will be adopted within 2 weeks? In other words, what is the probability that the sample proportion of animals adopted within two weeks of their arrival is at least 0.65? a) 0.0748 b) 0.0899 c) 0.1041 d) 0.9101 50) z is a standard normal random variable. Find P(1.3 ≤ z ≤ 2.4). a) 0.0886 b) 0.1428 c) 0.8572 d) 0.9114 51) The weight of an object is an example of a) a discrete random variable. b) either a continuous or a discrete random variable, depending on the nature of the object. c) a continuous random variable. d) either a continuous or a discrete random variable, depending on the unit of measurement. 52) The mean of a sample a) is not impacted by extremely high or low values. b) is not unique. c) cannot be calculated for categorical data. d) is calculated after arranging all the data from low to high 53) The standard deviation a) measures dispersion around the mode. b) represents the square of the variance. c) is measured in the same units as the mean. d) is not greatly impacted by outliers. 54) The relative frequency of a class is computed by a) dividing the midpoint of the class by the sample size. b) dividing the frequency of the class by the midpoint. c) dividing the frequency of the class by the sample size. d) dividing the sample size by the frequency of the class. 55) Which is the cost of a shirt an example of? a) categorical data b) either categorical or quantitative data c) quantitative data d) nominal data