STAT
Exam2_A_F18_Key.pdf

The consulting group collects information on 50

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’s claim. The consulting group collects information on 50 randomly selected U.S. assistant professors’ salaries and the data obtained is presented in the JMP output below. Use this output to answer the following questions. Round your final answers to the nearest 2 decimal places. Distributions Salary 60000 65000 70000 75000 80000 85000 90000 95000 Summary Statistics Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N 81690 8973.3 1269 50 Test Mean Hypothesized Value Actual Estimate DF Std Dev Test Statistic Prob > |t| Prob > t Prob < t t Test 0.0055* 0.0027* 0.9973 74000 76000 78000 80000 82000 (a) [2pts.] Describe in words what the population mean represents in the context of the problem. The true average salary of assistant professors in the U.S. - Form A and Form B (b) [4pts.] Let μ be the population mean. State the null and the alternative hypotheses using proper statistical notation and using the appropriate values from the problem statement: H 0 : μ = 78 , 000 vs H a : μ 6 = 78 , 000 - Form A H 0 : μ = 75 , 000 vs H a : μ 6 = 75 , 000 - Form B (c) [5pts.] Calculate the value of the test statistic to test the hypothesis in part (3b). Show your work here: t = 81690 - 78000 8973 . 3 / 50 = 2 . 91 Form A t = 77375 - 75000 6008 / 50 = 2 . 79 Form B MAX=11
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Exam II Stat 226 Fall 2018 – FORM A : KEY Page 7 (d) [3pts.] Using the JMP output provided, report here the p -value for the test in part (3b) and circle a correct interpretation of this value. p -value: 0.0055 - Form A 0.0074 - Form B Circle the correct interpretation of the above p -value: i. The probability of obtaining an absolute value of the test-statistic at least as extreme as the observed one assuming H 0 holds true. Form A and Form B ii. The probability of obtaining a value of the test-statistic at least as large as the observed one assuming H 0 holds true. iii. The probability of obtaining a value of the test-statistic at least as small as the observed one assuming H 0 holds true. iv. None of the above. (e) [2pts.] Make a decision at a significance level of 0.05. (Circle one and fill in the blank:) Reject H 0 , since p < 0 . 05 Form A and Form B Fail to reject H 0 , since (f) [1pt.] According to the analysis conducted in this problem, which of the following state- ments is more reasonable (check one): Form A i. The true mean salary of assistant professors at U.S. universities is not $78,000. ii. The true mean salary of assistant professors at U.S. universities is $78,000. Form B i. The true mean salary of assistant professors at U.S. universities is $75,000. ii. The true mean salary of assistant professors at U.S. universities is not $75,000. 4. [5pts.] Circle T or F to indicate which of these statements are TRUE and which ones are FALSE . Form A: F T T T F Form B: T F T F T (a) T F We are 90% confident that a correctly constructed 90% confidence interval for the true population mean will include the sample mean. sample mean population mean (b) T F The midpoint of a confidence interval for the population mean is the sample mean. See construction of CIs. (c) T F With a large enough sample size, the null hypothesis H 0 : μ = μ 0 (with the alternative hypothesis H a : μ 6 = μ 0 ) will almost always be rejected. Practical vs Statistical Significance (d) T F The probability of a Type I error is the significance level α .
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  • Spring '08
  • ABBEY
  • Statistical hypothesis testing

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