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Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 1. If the test value in the figure below, for a test of the difference between two large sample means, is 2.57 when the critical value is 1.96, what decision about the hypothesis should be made? A) reject the null hypothesis C) reject the alternative hypothesis B) accept the null hypothesis D) not enough information Ans: A Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-3 2. 1 2 n2 n1 The standard error of difference of two large sample means is . Ans: False Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-2 3. In the figure below, if the z -test value is 1.43 for a test of the difference between two large sample means, then the null hypothesis should not be rejected. Ans: True Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-3 4. When hypothesizing a difference of 0, if the confidence interval does not contain 0, the null hypothesis is rejected. Ans: True Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-4 5. For normally distributed populations, if two samples are independent and the variances are known, the z -test is used. Ans: True Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-3 Page 108 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 6. A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectivess for women and for men. At α = .05, what is the test value? Women Men Sample size 70 70 Mean effect 8.5 8.65 Sample variance 2.5 4.5 A) –1.50 B) 0.32 C) –2.11 D) –0.47 Ans: D Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-6 7. The campus bookstore asked a random set of freshmen and seniors as to how much they spent on textbooks in that term. The bookstore believes that the two groups spend the same amount. What is the test value? Freshmen Seniors Sample size 70 60 Mean spending 40 25 Sample variance 400 800 A) 0.79 B) 4.36 C) 3.44 D) 2.00 Ans: C Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-6 Use the following to answer questions 8-10: A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. Africa Asia X 55.3 65.2 8.1 9.3 n 53 42 8. What is the null hypothesis? Use 0.05 . A) H0 : 1 2 B) H0 : 1 2 C) H0 : 1 2 D) H0 : 1 2 Ans: B Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-6 9. Calculate the critical value. Use 0.05 . A) –1.65 B) –2.33 C) –2.58 D) –1.96 Ans: A Difficulty: Easy Objective: 1 Section: 2 Similar Exercise: 9-2-6 10. What is the test value? Use 0.05 . A) –6.86 B) –3.70 C) –4.13 D) –5.45 Ans: D Difficulty: Moderate Objective: 1 Section: 2 Similar Exercise: 9-2- 6 Page 109 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 11. Determine the 95% confidence interval of the true difference in the means. A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. Use 0.05 . Africa Asia X 55.3 65.2 8.1 9.3 n 53 42 A) 1216 1 2 6.86 . C) 1135 1 2 7.58 . B) 13.46 1 2 6.34 D) 16.33 1 2 5.98 Ans: B Difficulty: Moderate Objective: 1 Section: 2 Similar Exercise: 9-2- 19 12. The formula for the z -test for comparing two means from independent populations is __________. Ans: X 1 X 2 1 2 t 12 2 2 n1 n2 Difficulty: Moderate Objective: 1 Section: 2 Similar Exercise: 9-2-2 13. Joan moves into her new apartment and wants to purchase a new couch. She wants to determine if there is any difference between the average costs of couches at two different stores. Test the hypothesis that there is no difference at 0.05 . Store 1 Store 2 x $650 $730 $61 $78 n 24 21 Ans: H0: 1 2 H1: 1 2 . Critical Value = ±1.96; z 3.79 . Reject H0 . There is a difference in price between the two stores. Difficulty: Moderate Objective: 1 Section: 2 Similar Exercise: 9-2-6 14. A conservationist wants to know if the average water level in Horseshoe Lake is more than the average water level in Swan Lake. Test his hypothesis at 0.01 . Horseshoe Lake Swan Lake x 43 38 3.2 2.4 n 23 23 Ans: H0 : 1 2 H1: 1 2 Critical Value = 2.33, z 5.99 . Reject H0 . It appears that the average water level in Horseshoe Lake is more than the average water level in Swan Lake. Difficulty: Moderate Objective: 1 Section: 2 Similar Exercise: 9-2-6 Page 110 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 15. A marketing firm asked a random set of married and single men as to how much they were willing to spend for a vacation. At α = .05, is a difference in the two amounts? Married men Single men Sample size 60 40 Mean spending 420 405 Sample variance 5500 8000 A) No, because the test value 0.05 is inside the interval (-1.96, 1.96) B) No, because the test value 0.88 is inside the interval (-1.96, 1.96) C) No, because the test value 1.45 is inside the interval (-1.96, 1.96) D) No, because the test value 1.45 is outside the interval (-1.96, 1.96) Ans: B Difficulty: Moderate Objective: 1 Section: 2 Similar Exercise: 9-2- 6 16. A bond analyst is analyzing the interests rates for equivalent municipal bonds issued by two different states. At α = .05, is there a difference in the interest rates paid by the two states? State A State B Sample size 40 50 Mean interest rate (%) 3.9 4.35 Sample variance 0.03 0.04 A) Yes, because the test value –11.43 is outside the interval (-1.96, 1.96) B) Yes, because the test value –2.90 is outside the interval (-1.96, 1.96) C) Yes, because the test value 130.65 is outside the interval (-1.96, 1.96) D) No, because the test value –0.01 is inside the interval (-1.96, 1.96) Ans: A Difficulty: Moderate Objective: 1 Section: 2 Similar Exercise: 9-2- 6 17. An educational researcher is analyzing the test scores for statistics students taught using two different methods - a traditional method and a web-based self-paced method. Can he conclude, at α = .05, that the test scores in the web-based self-paced method are lower? Traditional Web-based Self-paced Sample size 40 80 Mean test score 80 77 Sample variance 28 32 A) The data does not support the claim because the test value 1.36 is less than than 1.64. B) The data does not support the claim because the test value 1.36 is less than than 1.96. C) The data supports the claim because the test value 2.86 is greater than than 1.96. D) The data supports the claim because the test value 2.86 is greater than than 1.64. Ans: D Difficulty: Hard Objective: 1 Section: 2 Similar Exercise: 9-2-6 Page 111 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 18. An field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at α = .10, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree? Pine trees Spruce trees Sample size 80 60 Mean trunk diameter (cm) 45 42 Sample variance 140 180 A) The data does not support the claim because the test value 0.63 is less than than 1.28. B) The data does not support the claim because the test value 1.38 is greater than than 1.28. C) The data does not support the claim because the test value 1.38 is less than than 1.64. D) The data does not support the claim because the test value 0.63 is less than than 1.64. Ans: B Difficulty: Hard Objective: 1 Section: 2 Similar Exercise: 9-2-6 19. The value of F cannot be negative, because variances are always positive or zero. Ans: True Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-4 20. When finding the F -test value, the smaller of the variances is placed in the numerator. Ans: False Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-1 21. When comparing two variances or standard deviations, a t -test is used. Ans: False Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-1 22. The critical value for a one-tailed right F -test is 2.57, when 0025 , the degrees of . freedom for the numerator = 15, and the degrees of freedom for the denominator = 20. Ans: True Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-5 23. The critical value for a two-tailed F -test is 2.65, when 0.05 , the sample size from which the variance for the numerator was obtained = 10, and the sample size from which the variance for the denominator was obtained = 15. Ans: False Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-5 24. The mean value of F is approximately equal to __________. Ans: one Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-4 25. To determine whether two sample variances are equal, a researcher can use a(n) __________. Ans: F-test Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-4 Page 112 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 26. In comparing the two variances below, what is the test value and what are the degrees of freedom that should be used? Variance Number of values Sample 1 7 17 Sample 2 9 28 A) test value = 0.78, degrees of freedom = 17 and 28 B) test value = 0.78, degrees of freedom = 16 and 27 C) test value = 1.29, degrees of freedom = 16 and 27 D) test value = 1.29, degrees of freedom = 17 and 28 Ans: C Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-7 27. For the samples summarized below, test the hypothesis at α =.05 that the two variances are equal. Variance Number of data values Sample 1 19 8 Sample 2 7 18 A) Accept the hypothesis because the test value 2.71 is less than the critical value 3.16. B) Reject the hypothesis because the test value 2.71 is less than the critical value 3.16. C) Reject the hypothesis because the test value 7.37 is greater than the critical value 3.01. D) Reject the hypothesis because the test value 7.37 is greater than the critical value 3.01. Ans: A Difficulty: Easy Objective: 2 Section: 3 Similar Exercise: 9-3-7 28. What is the critical value for a two-tailed F -test with 010 , when the sample size . from which the variance for the numerator was obtained was 10, and the sample size from which the denominator was obtained was 24? A) 2.27 B) 2.25 C) 2.32 D) 2.30 Ans: C Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3- 5 29. Compute the critical value for a right-tailed F -test with 0.05 , d.f.N. = 21, and d.f.D. = 20. A) 2.12 B) 2.23 C) 2.20 D) 2.16 Ans: A Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3- 5 30. A car salesman claims that the variance of prices on convertibles is higher than the variance on station wagons. The standard deviation of 16 convertibles is $6800 and the standard deviation of 24 station wagons is $3900. For 0.05 , what is the test value? A) 3.00 B) 3.04 C) 2.78 D) 2.33 Ans: B Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3- 8 Page 113 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 31. A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount of money spent on lunches. The variance of nine business dinners was $6.12 and the variance of 12 business lunches was $0.87. What is the test value? A) 3.1 B) 9.61 C) 49.5 D) 7.03 Ans: D Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3- 8 32. A researcher hypothesizes that the variation in the car rental rates at a major cities' airport is less than the car rental rates in that city. The variance of 10 airport car rental rates was $25 and the variance of 4 city car rental rates was $60. What is the test value? A) 6.00 B) 1.55 C) 2.40 D) 5.76 Ans: C Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3- 8 33. Determine the value of as shown in the figure below, if the degrees of freedom were seven and nine. A) 0.01 B) 0.025 C) 0.05 D) 0.1 Ans: B Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3- 5 34. If the variances are not known and one or both sample sizes are less than 30, the F -test must be used. Ans: False Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3-4 Page 114 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 35. If s1 12.31 and F 2.13 , what is the value of s2 as shown in the figure below? A) 5.78 B) 8.43 C) 71.14 D) 17.97 Ans: B Difficulty: Moderate Objective: 2 Section: 3 Similar Exercise: 9-3- 5 36. For the samples summarized below, test the hypothesis at α =.05 that the two variances are equal. Variance Number of data values Sample 1 26 7 Sample 2 11 17 A) Accept the hypothesis because the test value 5.59 is greater than the critical value 3.34. B) Reject the hypothesis because the test value 2.36 is less than the critical value 3.16. C) Reject the hypothesis because the test value 5.59 is greater than the critical value 3.16. D) Accept the hypothesis because the test value 2.36 is less than the critical value 3.34. Ans: D Difficulty: Hard Objective: 2 Section: 3 Similar Exercise: 9-3-7 37. In comparing the two standard deviations below, what is the test value and what are the degrees of freedom that should be used? Standard Deviation Number of values Sample 1 5 20 Sample 2 4 28 A) test value = 1.25, degrees of freedom = 20 and 28 B) test value = 1.25, degrees of freedom = 19 and 27 C) test value = 1.56, degrees of freedom = 20 and 28 D) test value = 1.56, degrees of freedom = 19 and 27 Ans: C Difficulty: Hard Objective: 2 Section: 3 Similar Exercise: 9-3-7 38. A pooled estimate of the variance is a weighted average of the variance using the two sample variances and the __________ of each variance as the weights. Ans: degrees of freedom Difficulty: Easy Objective: 3 Section: 4 Similar Exercise: 9-3-3 Page 115 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 39. A college class believes that the average grade average of psychology students and the average grade averages of biology students are different. The class found that the actual grade averages of a sample of 12 psychology students was 3.5 and the average grade average of a sample of 11 biology students was 3.6. What is the null hypothesis for this study? A) H0 : 3.5 and 3.6 B) H0 : psycho log y 3.5 and H0 : bio log y 3.6 C) H0 : psycho log y bio log y 7.1 D) H0 : psycho log y bio log y Ans: D Difficulty: Easy Objective: 3 Section: 4 Similar Exercise: 9-4-1 Use the following to answer questions 40-42: Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine. The data obtained is shown in the table below. Imported Wine Domestic Wine X 7.03 9.78 s 2.31 3.62 n 15 16 40. What is the null hypothesis? Use 0.05 . A) H0 : 1 2 B) H0 : 1 2 C) H0 : 1 2 D) H0 : 1 2 Ans: B Difficulty: Easy Objective: 3 Section: 4 Similar Exercise: 9-4-1 41. What is the critical value? Use 0.05 . A) –1.761 B) –2.045 C) –1.697 D) –1.703 Ans: A Difficulty: Moderate Objective: 3 Section: 4 Similar Exercise: 9-4- 1 42. What is the test value? Use 0.05 . (Use the variances unequal formula) A) –6.97 B) –2.50 C) –4.53 D) –2.54 Ans: D Difficulty: Moderate Objective: 3 Section: 4 Similar Exercise: 9- Rev-10 43. The formula for the t - test for comparing two means (independent samples, variances equal) is: t X 1 X 2 1 2 . 2 s s2 1 2 n1 n2 Ans: False Difficulty: Moderate Objective: 3 Section: 4 Similar Exercise: 9-4-1 Page 116 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 44. In testing the equality of the two means below, what is the test statistic? (Use the unequal variances formula) Sample 1 Sample 2 Sample size 10 11 Sample mean 80 75 Sample variance 600 100 A) 2.26 B) 0.17 C) 0.07 D) 0.60 Ans: D Difficulty: Moderate Objective: 3 Section: 4 Similar Exercise: 9- Rev-10 45. In testing the equality of the two means below, what is the test statistic? (Use the equal variances formula) Sample 1 Sample 2 Sample size 13 9 Sample mean 55 80 Sample variance 600 400 A) –2.53 B) –1.50 C) –0.26 D) –2.31 Ans: A Difficulty: Moderate Objective: 3 Section: 4 Similar Exercise: 9-4- 1 46. A local charity thinks that people in River Heights give more money to their charity than people in Lakeview. They conducted a survey of 24 people in each subdivision and recorded the results. Is their hypothesis correct? Let 0.01 . River Heights Lakeview x $35 $25 s $5 $8 n 24 24 Ans: F -test: H 0 : 1 2 ; C.V. = 3.02; Fail to reject H 0 , therefore it can be assumed 2 2 that the variances are equal. t-test: H0 : 1 2 H1 : 1 2 , t = 5.20, C.V.= 2.500 , reject H0. There is enough evidence to support the claim that River Heights donates more money. Difficulty: Hard Objective: 3 Section: 4 Similar Exercise: 9-4-1 Page 117 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 47. Donaldson Corporation wants to hire a temporary secretary. There are two employment agencies in town, and it is believed that the average hourly wage charged by both agencies are the same. Test this claim at 0.05 . Agency A Agency B x $6.25 $6.55 s $0.40 $0.58 n 18 20 Ans: F-test: H0 : 1 2 ; C.V. = 2.62; Fail to reject H , therefore it can be assumed 2 2 0 that the variances are equal. t-test H0 : 1 2 H1 : 1 2 , t = -1.84, C.V. = 2.110 , fail to reject reject H0. There is not enough evidence to support the claim that the two agencies are not the same. Difficulty: Hard Objective: 3 Section: 4 Similar Exercise: 9-4-1 48. A marketing firm asked a random set of married women and married men as to how much they were willing to spend for jewelry as a present to their spouse. Can the firm conclude, at α = .05, that the two groups have different willingness to spend? (Use the unequal variances formula) Women Men Sample size 10 14 Mean spending amount 80 115 Sample variance 55 600 A) No, because the test value –0.72 is inside the interval (-2.23, 2.23) B) Yes, because the test value –5.03 is outside the interval (-2.26, 2.26) C) Yes, because the test value –10.91 is inside the interval (-2.23, 2.23) D) No, because the test value –10.91 is outside the interval (-2.26, 2.26) Ans: B Difficulty: Hard Objective: 3 Section: 4 Similar Exercise: 9-Rev-10 49. A reporter bought a hamburger at each of a set of random stores of two different restaurant chains. She then had the number of calories in each hamburger measured. Can the reporter conclude, at α = .05, that the two sets of hamburgers have a different number of categories? (Use the equal variances formula) Women Men Sample size 7 8 Mean spending amount 80 95 Sample variance 450 900 A) No, because the test value –0.08 is inside the interval (-2.14, 2.14) B) No, because the test value –0.08 is inside the interval (-2.16, 2.16) C) No, because the test value –1.10 is inside the interval (-2.16, 2.16) D) No, because the test value –2.00 is inside the interval (-2.16, 2.16) Ans: C Difficulty: Hard Objective: 3 Section: 4 Similar Exercise: 9-4-2 50. When subjects are matched according to one variable, the matching process does not eliminate the influence of other variables. Ans: True Difficulty: Easy Objective: 4 Section: 5 Similar Exercise: 9-5-1 Page 118 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 51. Samples are independent when they are not related. Ans: True Difficulty: Easy Objective: 4 Section: 5 Similar Exercise: 9-5-1 52. A medical researcher is interested in whether patients' left arms or right arms are longer. If 9 patients participate in this study (so that n left arms and n left arms are measured), how many degrees of freedom should the researcher use in her t-test critical value? A) 8 B) 9 C) 16 D) 17 Ans: A Difficulty: Easy Objective: 4 Section: 5 Similar Exercise: 9-5-2 53. When the subjects are paired or matched in some way, samples are considered to be __________. Ans: dependent Difficulty: Easy Objective: 4 Section: 5 Similar Exercise: 9-5-1 Use the following to answer questions 54-57: A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Miles / Gal Without Miles / Gal With 21.2 23.8 25.4 25.6 20.9 22.4 27.6 28.3 22.8 24.5 27.3 28.8 23.4 25.2 54. State the alternative hypothesis? A) H1: D 0 B) H1: D 0 C) H1: D 0 D) H1: D 0 Ans: C Difficulty: Easy Objective: 4 Section: 5 Similar Exercise: 9-5-2 55. Determine the mean of the difference. A) –0.96 B) –6.3 C) 1.43 D) –1.43 Ans: D Difficulty: Moderate Objective: 4 Section: 5 Similar Exercise: 9-5- 2 56. Compute the standard deviation of the difference. A) 0.78 B) 0.69 C) 0.87 D) 0.48 Ans: A Difficulty: Moderate Objective: 4 Section: 5 Similar Exercise: 9-5- 2 Page 119 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 57. What is the critical value using 0.05 ? A) -1.782 B) -1.761 C) -1.943 D) -1.895 Ans: C Difficulty: Moderate Objective: 4 Section: 5 Similar Exercise: 9-5- 2 58. If the samples are dependent, the t - test for dependent samples is used. Ans: True Difficulty: Moderate Objective: 4 Section: 5 Similar Exercise: 9-5-1 59. The formula of the t -test for dependent samples is __________. Ans: D D t sD n Difficulty: Moderate Objective: 4 Section: 5 Similar Exercise: 9-5-1 60. The critical value for a left-tailed t-test for dependent samples is __________ when the degrees of freedom = 7 and 0025 . . Ans: –2.365 Difficulty: Moderate Objective: 4 Section: 5 Similar Exercise: 9-5-2 61. A running coach wanted to see whether runners ran faster after eating spaghetti the night before. 14 random runners were chosen for this study. They ran a 5 kilometer race after having a normal dinner the night before, and then a week later, reran the same race after having a spaghetti dinner the night before. Their results (in seconds) are in the table below. At α = .01, what is the test value to use for this test? Regular Dinner Spaghetti Difference Dinner by runner Sample mean 940 930 –10 Sample variance 3000 2000 450 A) –1.87 B) –0.47 C) –0.14 D) –1.76 Ans: D Difficulty: Moderate Objective: 4 Section: 5 Similar Exercise: 9-5- 2 Page 120 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 62. A dietician investigated whether apples washed in hot water or in cold water turned brown at different rates when exposed to air. She took 11 random apples and cut each in half. She washed one half of each apple in hot water and the other half in cold water, and then put both halves out in a tray. Her results (in hours until turning a particular shade of brown) are in the table below. At α = .01, did she see a difference between the two treatments? Hot Water Cold Water Difference by apple Sample mean 5.00 4.35 –0.65 Sample variance 1.60 2.00 0.55 A) No, because the test value –0.83 is inside the range (-3.11, 3.11). B) No, because the test value –2.91 is inside the range (-3.17, 3.17). C) No, because the test value –2.91 is inside the range (-3.11, 3.11). D) No, because the test value –0.83 is inside the range (-3.17, 3.17). Ans: B Difficulty: Hard Objective: 4 Section: 5 Similar Exercise: 9-5-2 63. One of the requirements for the z - test for comparing two proportions is that the samples must be dependent on each other. Ans: False Difficulty: Easy Objective: 5 Section: 6 Similar Exercise: 9-6-3 64. One poll found that 43% of male voters will support a candidate while another found that 49% of female voters will be in support. To test whether this candidate has equal levels of support between male and female voters, the null hypothesis should be A) H0 : pmale pfemale C) H0 : pmale 43%, H0 : pfemale 49% B) H0 : pmale 50%, H0 : pfemale 50% D) H0 : pmale pfemale Ans: A Difficulty: Easy Objective: 5 Section: 6 Similar Exercise: 9-6-3 65. One poll found that 38% of male voters will support a candidate while another found that 44% of female voters will be in support. To test whether this candidate has equal levels of support between male and female voters, the alternative hypothesis should be A) H0 : pmale pfemale B) H0 : pmale 50%, H0 : pfemale 50% C) H0 : pmale 38%, H0 : pfemale 44% D) H0 : pmale pfemale Ans: D Difficulty: Easy Objective: 5 Section: 6 Similar Exercise: 9-6-3 66. Find p and q , if x1 23, n1 43, x2 29, and n2 52 . Ans: p 52 and q 43 95 95 Difficulty: Easy Objective: 5 Section: 6 Similar Exercise: 9-6-2 Page 121 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 67. Find p and q when X 1 =12, n1 =40, X 2 =20, and n2 =60 A) p = 0.32 and q = 0.68 C) p = 1.47 and q = 3.12 B) p = 3.12 and q = 1.47 D) p = 0.68 and q = 0.32 Ans: A Difficulty: Easy Objective: 5 Section: 6 Similar Exercise: 9-6-1 68. A recent survey reported that in a sample of 300 students who attend two-year colleges, 105 work at least 20 hours a week. In a sample of 225 students attending private universities, only 20 students work at least 20 hours per week. What is the test value? A) 6.95 B) 7.61 C) 2.38 D) 4.18 Ans: A Difficulty: Moderate Objective: 5 Section: 6 Similar Exercise: 9-6- 3 69. The standard error of difference in terms of the weighted estimate is __________ when testing the difference between two population proportions. Ans: 1 1 ( p p ) pq n1 n2 1 2 Difficulty: Moderate Objective: 5 Section: 6 Similar Exercise: 9-6-3 70. When testing the difference between two proportions, one sample had 30 out of 100 who were for capital punishment and the other sample had 60 out of 80 who were for capital punishment. Calculate the standard error. A) 0.075 B) 0.060 C) 0.042 D) 0.098 Ans: A Difficulty: Hard Objective: 5 Section: 6 Similar Exercise: 9-6-5 Page 122 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 71. 70% of students at a university live on campus. A random sample found that 31 of 50 male students and 41 of 50 of female students lived on campus. At the .05 level of significance, is there sufficient evidence to conclude that a difference exists between the proportion of male students who live on campus and the proportion of female students who live on campus? A) No, there is not sufficient information to reject the hypothesis that the proportion of male students who live on campus and the proportion of female students who live on campus are the same because the test value –0.20 is inside the acceptance region (-1.96,1.96). B) No, there is not sufficient information to reject the hypothesis that the proportion of male students who live on campus and the proportion of female students who live on campus are the same because the test value –1.21 is inside the acceptance region (-1.96,1.96). C) Yes, there is sufficient information to reject the hypothesis that the proportion of male students who live on campus and the proportion of female students who live on campus are the same because the test value –2.33 is outside the acceptance region (-1.96,1.96). D) Yes, there is sufficient information to reject the hypothesis that the proportion of male students who live on campus and the proportion of female students who live on campus are the same because the test value –2.23 is outside the acceptance region (-1.96,1.96). Ans: D Difficulty: Hard Objective: 5 Section: 6 Similar Exercise: 9-6-5 72. Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 16 of 40 at one school and 13 of 30 at the other had this infection. At the .05 level of significance, is there sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other? A) Yes, there is sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –2.35 is outside the acceptance region (-1.96,1.96). B) No, there is not sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –0.28 is inside the acceptance region (-1.96,1.96). C) No, there is not sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –0.37 is inside the acceptance region (-1.96,1.96). D) No, there is not sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –1.32 is inside the acceptance region (-1.96,1.96). Ans: B Difficulty: Hard Objective: 5 Section: 6 Similar Exercise: 9-6-5 Page 123 Chapter 9 - Testing the Difference Between Two Means, Two Variances, and Two Proportions 73. A study of cats and dogs found that 16 of 50 cats and 32 of 55 dogs slept more than 10 hours per day. At the .05 level of significance, is there sufficient evidence to conclude that a difference exists between the proportion of cats and the proportion of dogs that sleep more than 10 hours per day? A) Yes, there is sufficient information to reject the hypothesis that the proportion of cats and the proportion of dogs that sleep more than 10 hours per day are the same because the test value –2.69 is outside the acceptance region (-1.96,1.96). B) No, there is not sufficient information to reject the hypothesis that the proportion of cats and the proportion of dogs that sleep more than 10 hours per day are the same because the test value –1.76 is inside the acceptance region (-1.96,1.96). C) Yes, there is sufficient information to reject the hypothesis that the proportion of cats and the proportion of dogs that sleep more than 10 hours per day are the same because the test value –3.11 is outside the acceptance region (-1.96,1.96). D) No, there is not sufficient information to reject the hypothesis that the proportion of cats and the proportion of dogs that sleep more than 10 hours per day are the same because the test value –0.84 is inside the acceptance region (-1.96,1.96). Ans: A Difficulty: Hard Objective: 5 Section: 6 Similar Exercise: 9-6-5 Page 124