Homework 6 instructions

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Purdue University *

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355

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Statistics

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Apr 3, 2024

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Uploaded by ElderPower13381

STAT 355: Homework 6 For the questions below, show all of your code, any corresponding output, and answer the questions. For questions 1- 3, you will need to access the data in hw5.csv on Brightspace -- it’s the same data as HW5. 1. A survey was taken of 25 Purdue students to see how many hours they spend using their mobile devices on a typical day. This data is stored in the column named purdue in hw5.csv. a. Perform a t -based hypothesis test at α = 0.05 to see if Purdue’s mean daily mobile hours differs from the national average of 4.37 hours. Clearly state the hypotheses, p -value, and the conclusion of the test. b. What critical value(s) would be used in the test in part a? c. Keeping everything else the same, how would a larger sample size affect part a’s p -value? d. Perform a two-sided Wilcoxon test at α = 0.05 to compare Purdue to the national average of 4.37 hours. Report the p -value and the conclusion of the test. How do these compare to part a? 2. Data in the column named iu in hw5.csv is from a sample of 20 IU students who were asked the same question about mobile device usage as the Purdue students in question 1. We wish to compare the means for Purdue students and IU students. a. Perform a t -based hypothesis test at α = 0.05 to see if IU’s mean is higher than Purdue’s mean. Clearly state the hypotheses, p -value, and the conclusion of the test. b. Perform the corresponding Wilcoxon test at α = 0.05. Report the p -value and the conclusion of the test. How do these compare to part a? 3. For each of 16 randomly selected board game accessories, I found their current price (in $) both online and at a local retailer. This data is in the columns named online and local in hw5.csv. Row 1 has the online & local prices for the first product, row 2 for the second, etc. a. Perform a t -based hypothesis test at α = 0.01 to see if the online price is lower than the corresponding local price on average. Clearly state the hypotheses, p -value, and the conclusion of the test. b. Perform the corresponding Wilcoxon test at α = 0.01. Report the p -value and the conclusion of the test. How do these compare to part a? 4. A survey is conducted to determine if a certain political candidate has a majority (> 50%) of the vote in an upcoming election. 663 of the 1250 polled voters indicated that they will vote for the candidate. a. Perform a hypothesis test to see if the candidate has the majority of the vote at α = 0.05. Clearly state the hypotheses, p -value, and the conclusion of the test. b. Back in Homework 5, you found a 90% confidence interval for the same situation. Notice that the α values used back then and used now in part a are different ( α = 0.10 for the CI vs. α = 0.05 for the HT). Despite this inconsistency in the values of α , should the conclusions drawn from the CI and HT be consistent? Why or why not? 5. 300 Marvel fans were asked if they planned to watch the upcoming Kraven the Hunter movie in the theater, and 77 said “yes.” Another group of 250 DC fans were also asked, and 42 said “yes.” Perform a hypothesis test at α = 0.05 to see if there is a difference in population proportions. Clearly state the hypotheses, p -value, and the conclusion of the test.

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