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MATH302 Statistics Quiz 4 Assume that in a hypothesis test with null hypothesis 0 H : = 13.0 at 0.05, that a value of 11.0 for the sample mean results in the null hypothesis not being rejected. That corresponds to a confidence interval result of A) The 95% confidence interval for the mean does not contain the value 13.0 B) The 95% confidence interval for the mean contains the value 11.0 C) There is insufficient information to conclude whether the 95% confidence interval for the mean contains or does not contain the value 13.0 D) The 95% confidence interval for the mean contains the value 13.0 2. Nationwide, the average waiting time until electric utility customer service representative answers a call is 300 seconds per call. The Gigantic Kilowatt Energy Company took a sample of 35 calls and found that, on the average, they answered in 240 seconds per call with a standard deviation of 50. Can the company claim that they are faster than the average utility? A) No, because –0.20 falls in the critical region B) Yes, because –7.10 falls in the critical region C) No, because –1.20 falls in the critical region D) Yes, because –0.20 falls in the critical region 3. If the observed value is 4, the expected value is 5, and the standard error is 4, then the test value used for the z test is equal to A) –1.00 B) 0.25 C) –0.25 D) 1.00 4. Using the z table in Table E of Appendix C, what are the critical values for a two-tailed test when 0.03 . A) ± 2.17 B) ± 2.05 C) ± 2.33 D) ± 1.88 5. The average speed of greyhound dogs is about 18.8 meters per second. A particular greyhound breeder claims that her dogs are faster than the average greyhound. In a sample of 45 of her dogs, they ran, on the average, 19.2 meters per second with a standard deviation of 1.4. Is her claim correct if she is willing to accept an error rate of 2.5 out of 100? A) Yes, because 1.92 falls in the noncritical region B) No, because 0.04 falls in the noncritical region C) Yes, because 0.04 falls in the noncritical region D) No, because 1.92 falls in the noncritical region 6. What is the critical t-value for a right-tailed test when .025and d.f. = 12? A) 0.695 B) 2.179 C) 2.831 D) 2.201 7. Are the following statements a valid pair of null and alternative hypothesis? 0 H : 17 A H : 17 A) No, these statements both compare a parameter to a value B) No, there are no parameters contained in these statements C) No, the alternative hypothesis cannot contain numeric values D) No, these statements have overlapping regions 8. A doctor believes that the standard deviation of systolic blood pressure is 450. A random sample of 24 patients found a standard deviation of 520. Assume the variable is normally distributed and = 0.01. What are the critical values? A) 10.196 and 41.638 C) 9.262 and 44.181 B) 9.886 and 45.559 D) 10.856 and 42.980 9. A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a standard deviation of 1.2 or less. If 20 measurements are taken and their standard deviation is 1.8, is there enough evidence to reject the claim that her standard deviation is within the limit at _ = .01? A) No, comparing the test value 45.00 and the critical value 37.566. B) Yes, comparing the test value 42.75 and the critical value 36.191. C) Yes, comparing the test value 45.00 and the critical value 37.566. D) No, comparing the test value 42.75 and the critical value 36.191. 10. According to Beautiful Bride magazine, the average age of a groom is now 26.2 years. A sample of 16 prospective grooms in Chicago revealed that their average age was 26.6 years with a standard deviation of 5.3 years. At = 0.05, what is the test value? A) .292 B) 21.535 C) 0.302 D) 0.985 11. Assume that in a hypothesis test with null hypothesis 0 H : = 14.0 at 0.05, that a value of 13.0 for the sample mean results in the null hypothesis not being rejected. That corresponds to a confidence interval result of A) The 95% confidence interval for the mean contains the value 14.0 B) The 95% confidence interval for the mean does not contain the value 14.0 C) There is insufficient information as to if the 95% confidence interval for the mean does or does not contain the value 13.0 D) The 0.05% confidence interval for the mean contains the value 13.0 12. For the conjecture "The average age of students in this class is 20", the null hypothesis is: A) H0: _ 20" B) H0: _ 20" C) H0: _ 20" D) H0: = 20" Use the following to answer question 13: A recent survey indicated that the average amount spent for breakfast by business managers was $7.58 with a standard deviation of $0.42. It was felt that breakfasts on the West Coast were higher than $7.58. A sample of 81 business managers on the West Coast had an average breakfast cost of $7.65. 13. At = 0.05, what is the test value? A) –1.5 B) 1.96 C) 1.64 D) 1.5 14. Are the following statements a valid pair of null and alternative hypothesis? 0H : = 7 A H : 7 A) No, the alternative hypothesis cannot contain numeric values B) Yes, these statements are two non-overlapping hypotheses and compare two parameters C) No, there are no parameters contained in these statements D) Yes, these statements are two non-overlapping hypotheses and compare a parameter to a value 15. Using the z table in Table E of Appendix C, determine the critical value for the lefttailed test with = 0.02. A) 2.05 B) - 2.33 C) - 2.05 D) 2.33 Use the following to answer questions 16-17: The Eagle Ridge Contractors Association claims the average price of a home in their subdivision is $125,150 with a standard deviation of $7,350. A sample of 36 homes for sale in this subdivision had an average selling price of $123,550. Is there evidence that the costs of homes for sale in this subdivision are actually lower than claimed? 16. What is the p-value for a one-sided test of the data provided above? A) 0.0036 B) 0.1327 C) 0.0853 D) 0.0951 17. At = 0.05, what is the test value? A) 1.31 B) –1.52 C) 1.52 D) –1.31 18. Using the z table in Table E of Appendix C, determine the critical value for the righttailed test with = 0.035. A) 1.81 B) 0.39 C) 2.11 D) 2.05 19. Using the z-table (Table E), find the critical value (or values) for a = .14 right-tailed test. A) .1406 B) 1.08 C) 0.0557 D) 1.54 20. At a certain university, the average cost of books per student was $400 per student last semester. In a sample of 40 students this semester, their average cost was $430 with a standard deviation of $80. The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis? A) 15.00 B) 2.37 C) 0.38 D) 0.75 Use the following to answer questions 21-22: 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 (1) Asia (2) X 55.3 65.2 8.1 9.3 n 53 42 21. What is the null hypothesis? Use 0.05 . A) H0:1 2 B) H0:1 2 C) H0:1 2 D) H0:1 2 22. Calculate the critical value. Use 0.05 . A) –2.33 B) –2.58 C) –1.96 D) –1.645 23. 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 _ = .05, is a difference in the two amounts? Married men Single men Sample size 50 70 Mean spending 260 185 Sample variance 4500 9000 A) Yes, because the test value 5.07 is outside the interval (-1.96, 1.96) B) No, because the test value 2.00 is outside the interval (-1.96, 1.96) C) No, because the test value 0.34 is inside the interval (-1.96, 1.96) D) Yes, because the test value 2.00 is inside the interval (-1.96, 1.96) 24. For the samples summarized below, test the hypothesis at _ =.05 that the two variances are equal. Variance Number of data values Sample 1 19 8 Sample 2 9 18 A) Reject the hypothesis because the test value 2.11 is less than the critical value 3.16. B) Reject the hypothesis because the test value 4.46 is greater than the critical value 3.01. C) Do not reject the hypothesis because the test value 2.11 is less than the critical value 3.16. D) Do not reject the hypothesis because the critical value 3.01 is greater than the test value 4.46. 25. A medical researcher is interested in whether patients' left arms or right arms are longer. If 14 patients participate in this study (so that n left arms and n right arms are measured), how many degrees of freedom should the researcher use in her t-test critical value assuming that the variances are equal? A) 13 B) 27 C) 14 D) 26 26. 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 42 at one school and 21 of 36 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) 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 –1.78 is inside the acceptance region (-1.96,1.96). B) 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 –2.34 is outside the acceptance region (-1.96,1.96). C) 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 –8.76 is outside the acceptance region (-1.96,1.96). D) 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 –15.73 is outside the acceptance region (-1.96,1.96). 27. Determine the value of as shown in the figure below, if the degrees of freedom were seven and nine. A) 0.1 B) 0.01 C) 0.025 D) 0.05 28. 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 effectiveness for women and for men. At _ = .05, what is the test value? Women Men Sample size 40 70 Mean effect 7 6.75 Sample variance 2.5 4.5 A) 0.70 B) 1.97 C) 0.36 D) 1.42 29. 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 9 12 Sample mean 80 115 Sample variance 550 100 A) –4.20 B) –2.31 C) –0.18 D) –0.50 Use the following to answer question 30: 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 25.230. State the alternative hypothesis? A) H1: D _ 0 B) H1: D < 0 C) H1: D = 0 D) H1: D _ 0 31. 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 12 8 Sample mean 115 80 Sample variance 700 450 A) 0.28 B) 3.27 C) 2.37 D) 0.14 32. 66% of students at a university live on campus. A random sample found that 20 of 40 male students and 40 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 –1.65 is inside the acceptance region (-1.96,1.96). B) 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 –3.15 is outside 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 –3.00 is outside the acceptance region (-1.96,1.96). D) 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 –0.30 is inside the acceptance region (-1.96,1.96). 33. For the samples summarized below, test the hypothesis at _ =.05 that the two variances are equal. Variance Number of data values Sample 1 30 9 Sample 2 10 19 A) Reject the hypothesis because the test value 9.00 is greater than the critical value 2.51. B) Do not reject the hypothesis because the test value 9.00 is greater than the critical value 3.01. C) Do not reject the hypothesis because the test value 3.00 is less than the critical value 3.01. D) Reject the hypothesis because the test value 3.00 is greater than the critical value 2.51 34. A bond analyst is analyzing the interest rates for equivalent municipal bonds issued by two different states. At _ = .05, is there a difference in the interest rates paid by the two states? State A State B Sample size 80 70 Mean interest rate (%) 3.7 4.25 Sample variance 0.02 0.03 A) No, because the test value –0.02 is inside the interval (-1.96, 1.96) B) Yes, because the test value 445.79 is outside the interval (-1.96, 1.96) C) Yes, because the test value –21.11 is outside the interval (-1.96, 1.96) D) Yes, because the test value –8.11 is outside the interval (-1.96, 1.96) 35. One poll found that 44% of male voters will support a candidate while another found that 50% 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) 1 male H : p 50%, 1 female H : p 50% C) 1 male female H : p p B) 1 male H : p 44%, 1 female H : p 50% D) 1 male female H : p p 36. 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) 13.46 1 2 6.34 C) 12.16 1 2 6.86 B) 16.33 1 2 5.98 D) 11.35 1 2 7.58 37. 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 6 18 Sample 2 11 29 A) test value = 1.83, degrees of freedom = 18 and 29 B) test value = 1.83, degrees of freedom = 17 and 28 C) test value = 0.55, degrees of freedom = 18 and 29 D) test value = 0.55, degrees of freedom = 17 and 28 38. A study of cats and dogs found that 11 of 50 cats and 21 of 50 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) 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 –0.65 is inside the acceptance region (-1.96,1.96). B) 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 –2.14 is outside the acceptance region (-1.96,1.96). C) 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 –1.40 is inside the acceptance region (-1.96,1.96). D) 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 –2.47 is outside the acceptance region (-1.96,1.96). 39. A dietician investigated whether apples washed in hot water or in cold water turned brown at different rates when exposed to air. She took 13 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 _ = .01, did she see a difference between the two treatments? Hot Water Cold Water Sample mean 5.50 4.85 Sample variance 2.60 2.00 A) No, because the test value –1.09 is inside the range (-3.055, 3.055). B) No, because the test value –0.79 is inside the range (-3.055, 3.055). C) Yes, because the test value –0.79 is inside the range (-3.012, 3.012). D) Yes, because the test value –1.09 is outside the range (-3.012, 3.012). Use the following to answer question 40: 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 test value? Use = 0.05. (Use the variances unequal formula) A) –4.53 B) –2.54 C) –2.50 D) –6.97

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