The following table lists the difference in rankings for universities for MBA programs from 2023 to 2024. We are interested in testing to see if there is a significant difference between the rankings: College 2023 2024 University of Pennsylvania: Wharton 3 1 Insead 2 2 Columbia Business School 1 3 SDA 6 3 IESE Business School 3 5 Northwestern Kellogg School of Management 9 6 Question 8 Find the average difference, $\bar{d}$ A. 4 B. -4 C. 0.8 D. 0.6667 Question 9 Find $s_d$ A. 2.3381 B. 5.4667 C. 5.9111 D. 2.4313 Question 10 Find the test statistic. A. $t = 0.70$ B. $t = 0.70$ C. $t = 1.79$ D. $t = 1.79$ Question 11 What is the critical value at 98% confidence? A. $\pm 2.3263$ B. $\pm 1.96$ C. $\pm 2.5706$ D. $\pm 3.3649$ Question 12 What conclusion would be made here at 98% confidence? A. Reject $H_0$ B. Do not reject $H_0$
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Step 1: Calculate the differences in rankings for each university: University of Pennsylvania: Wharton: 3 - 1 = 2 Insead: 2 - 2 = 0 Columbia Business School: 1 - 3 = -2 SDA: 6 - 3 = 3 IESE Business School: 3 - 5 = -2 Northwestern Kellogg School of Management: 9 - 6 Show more…
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It is desired to compare the average test scores at the two schools. Suppose that random samples of college freshmen are selected from two universities: 15 students from school A and 17 students from school B. The summary statistics of a standardized test are given in the following table. Test if there is a difference in mean test scores at the two schools, assuming that test scores came from normal distributions. Use a 0.05 level of significance. Sample Size | Average Score | Standard Deviation ------------|---------------|------------------ School A (1) | 15 | 100 | 15 School B (2) | 17 | 90 | 18 Part A: What hypothesis test should be used? a. Independent samples t-test b. Matched pairs t-test c. Independent samples z-test d. Test for two proportions Part B: What are the null and alternative hypotheses? a. H0: mu1-mu2=0, Ha: mu1-mu2 <0 b. H0: mu1-mu2 not=0, Ha: mu1-mu2=0 c. H0: mu1-mu2=0, Ha: mu1-mu2 not=0 d. H0: mu1-mu2=0, Ha: mu1-mu2 >0 Part C: Compute the value of the pooled variance. a. 277.8 b. 15.6 c. 16.6 d. 260.4 Part D: Find the value of the test statistic. a. -1.694 b. -0.287 c. 1.694 d. 0.287 Part E: Find the rejection region. a. z<-1.960 and z>1.960 b. t<-1.697 and t>1.697 c. t>1.697 d. t<-2.042 and t>2.042 Part F: What is your decision? a. Do not reject H0, because the value of the test statistic falls in the rejection region. b. Do not reject H0, because the value of the test statistic does not fall in the rejection region. c. Reject H0, because the value of the test statistic does not fall in the rejection region. d. Reject H0, because the value of the test statistic falls in the rejection region. Part G: Interpret the conclusion in the context of the problem. At the 0.05 level of significance, a. There is not sufficient evidence of a difference in mean test scores between the two schools. b. There is not sufficient evidence that the mean test scores are equal. c. There is sufficient evidence that the mean test scores are equal. d. There is sufficient evidence of a difference in mean test scores between the two schools.
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It has been established that the average time it takes for students to complete a bachelor's degree is 4.8 years. In order to help students graduate earlier, a university wanted to implement a first-year seminar. But before the program is put in place for all their students, the university wants to get a sense of whether or not such a program would be effective. To test the program, the university conducted a pilot study by obtaining a random sample. When a total of 25 students graduated from the university, they found that the mean time to graduation was 4.3 with a standard deviation of 1.3 years. Q1: Which of the following is an appropriate alternative hypothesis? a) μ < 4.8 b) μ > 4.8 c) μ ≠4.8 d) μ = 4.8 Q2: Using the information from the previous problem, what is the approximate value of the test statistic? a) -1.71 b) -1.93 c) -1.15 d) -0.05 e) None of the above Q3: Using the information from the previous two problems, what is the value of t that defines the rejection region? a) -1.708 b) -2.060 c) -1.711 d) -2.064 e) None of the above Q4: Using the information from the previous problems, what is the best estimate of the p-value? a) 0.01 < p < 0.05 b) 0.05 < p < 0.10 c) 0 < p < 0.005 d) 0.50 < p e) 0.10 < p < 0.50
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