# finish a 26 problems set

1. A sample of 10 employees in the graphics department of Design, Inc. is selected. The employees’ ages are given as follows: 34 35 39 24 62 40 18 35 28 35 Compute the interquartile range of ages. a. 1 b. 11 c. 42 d. 44 e. None of these responses 2. The average grades of a sample of 8 statistics students and the number of absences they had during the semester are given as follows: Student # Absences Average Grade 1 1 94 2 2 78 3 2 70 4 1 88 5 3 68 6 4 40 7 8 30 8 3 60 Compute the sample covariance. a. -0.915 b. 2.268 c. 22.168 d. -46 e. None of these responses Answer questions 3 and 4 based on the following. A survey of business students who had taken the Graduate Management Admissions Test (GMAT) indicated that students who have spent at least five hours studying GMAT review guides have a probability of 0.85 of scoring above 400. Students who do not review in this way have a probability of 0.65 of scoring above 400. It has been determined that 70% of the business students review for the test. 3. Compute the probability of scoring above 400. a. 0.12 b. 0.20 c. 0.55 d. 0.79 e. 1.50 4. Given that a student scored above 400, what is the probability that he/she reviewed for the test? a. 0.15 b. 0.27 c. 0.60 d. 0.75 e. 0.85 5. The student body of a large university consists of 60% female students. A random sample of 8 students is selected. What is the probability that among the students in the sample at least 6 are male? a. 0.0413 b. 0.0079 c. 0.0007 d. 0.0499 6. In a large class, suppose that your instructor tells you that you need to obtain a grade in the top 10% of your class to get an A on Exam X. From past experience, your instructor is able to say that the mean and standard deviation on Exam X will be 72 and 13, respectively, and that grades are distributed normally. What will be the minimum grade needed to obtain an A? a. 88.64 b. 55.36 c. 73.28 d. 75.32 7. The travel time for a businesswoman traveling between Dallas and Fort Worth is uniformly distributed between 40 and 90 minutes. The probability that her trip will take exactly 50 minutes is a. 1.00 b. 0.02 c. 0.06 d. 0.20 e. 0.00 8. Consider the below population of percent tips. Would the sampling distribution of x̅ for n = 35 consist of the data point 17.09%, gotten by adding up the first seven columns of percent tips and dividing by 35? 15 20 16 16 16 15 20 18 10 20 17 18 19 20 20 15 20 19 20 15 17 15 20 19 17 20 17 20 18 15 10 17 20 20 18 15 15 19 15 16 11 20 15 18 20 17 10 20 15 20 a. Yes b. No 9. Refer to Question 8. Can we say that the sampling distribution of x̅ for n = 35 is distributed normally? a. Yes b. No 10. Refer to Question 8. Compute the expected value of x̅ (E(x̅)) associated with the sampling distribution of x̅ for n = 35. a. 16.40% b. 17.09% c. 17.16% d. 20.00% e. It is not possible to compute E(x̅) 11. A local health care facility noted that in a sample of 200 patients, 180 were referred to them by the local hospital. Provide a 99% confidence interval for all the patients who are referred to this facility by the hospital. a. 0.9 ± 0.013*0.021 b. 0.9 ± 2.575*0.021 c. 0.9 ± 2.601*0.021 d. 0.9 ± 2.601*0.00045 e. 0.9 ± 2.575*0.00045 Answer questions 12 – 15 based on the following. A supermarket wants to test whether the mean weight of the cans of peas sold by a particular maker equals 24 oz. It chooses a random sample of 16 cans and finds that the sample mean is 23.3 oz and the sample standard deviation is 0.4 oz. Your job is to test, at the 5% level of significance, whether or not the mean weight equals 24 oz. 12. What are the null and alternative hypotheses? a. Ho: µ = 24, Ha: µ ≠ 24 b. Ho: µ ≤ 24, Ha: µ > 24 c. Ho: µ ≥ 24, Ha: µ < 24 d. Ho: µ = 23.3, Ha: µ ≠ 23.3 13. Compute the p-value. When computing two-tailed p-values, remember to use the 2p approach! a. 0.00000214 b. 0.0503 c. 0.00000428 d. 0.1006 e. 0.2012 14. What is your conclusion? a. Reject the null hypothesis at the 5% level b. Fail to reject the null hypothesis at the 5% level c. Reject the null hypothesis at the 2.5% level d. Fail to reject the null hypothesis at the 2.5% level e. None of these responses 15. Compute the power of the test when µ = 24.1. a. 0.0037 b. 0.1480 c. 0.8520 d. 0.8557 e. 0.9963 Answer questions 16 – 17 based on the following. 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: Today Five Years Ago x̅ 82 88 σ 2 112.5 54 n 45 36 16. The 95% confidence interval for the difference between the two population means (Today – Five Years Ago) is a. -9.92 to -2.08 b. -3.08 to 3.92 c. -13.84 to -1.16 d. -24.77 to 12.23 e. 2.08 to 9.92 17. The statistics teacher wishes to test, using a two-tailed approach, the hypothesis of no difference between the population mean scores using a 5% level of significance. The p-value associated with this test is: When computing two-tailed p-values, remember to use the 2p approach! a. 0.0013 b. 0.0026 c. 0.4987 d. 0.9987 18. A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounces. A 95% confidence interval estimate for the variance of the population is a. 0.2313 to 0.8533 b. 0.2224 to 0.7924 c. 0.0889 to 0.3169 d. 0.0925 to 0.3413 Answer questions 19 – 20 based on the following. The standard deviation of the ages of a sample of 16 executives from northern states was 8.2 years, while the standard deviation of the ages of a sample of 25 executives from southern states was 12.8 years. At α = 0.10, test to see if there is any difference in the standard deviations of the ages of all northern and southern executives. 19. Compute the p-value associated with this test. When computing two-tailed p-values, remember to use the 2p approach! a. 0.0498 b. 0.0772 c. 0.1873 d. 0.3746 20. What is the probability of rejecting the null hypothesis when it is true? a. 1% b. 5% c. 10% d. None of these responses Answer questions 21 – 23 based on the following. Among 1,000 managers with degrees in business administration, the following data have been accumulated as to their fields of concentration: Position in Management Major Top Management Middle Management Management 300 200 Marketing 200 0 Accounting 100 200 Test, using α = 0.01, to determine if their position in management is independent of their major. 21. What is your test statistic? a. -0.11 b. 25,600 c. 222.22 d. 14.91 22. Compute the critical value. a. 0.02 b. 0.00 c. 4.61 d. 9.21 e. 16.81 23. What is your conclusion? a. Reject the null at the 1% level b. Fail to reject the null at the 1% level c. Reject the null at the 0.5% level d. Fail to reject the null at the 0.5% level Answer questions 24 – 26 based on the following. In order to compare the life expectancies of three different brands of printers, 8 printers of each brand were randomly selected. Information regarding the 3 brands is shown below. Brand A Brand B Brand C Average Life (Months) 62 52 60 Sample Variance 36 25 49 At the 5% level of significance, test to see whether the mean life is the same across these brands. 24. Compute the p-value associated with your test statistic. When computing two-tailed p-values, remember to use the 2p approach! a. 0.0081 b. 0.0162 c. 0.0213 d. 0.0426 e. 0.1499 25. Compute Fisher’s LSD using Bonferroni’s adjusted α (set αEW = 0.05). a. 5.211 b. 6.298 c. 7.848 d. 23.790 e. 51.244 26. Fisher’s LSD procedure suggests that µA __ µB, µB __ µC, and µA __ µC. a. >, >, > b. <, <, < c. =, =, = d. >, <, = e. <, >, =