1. One- versus Two-Sample T-Test For each scenario, choose paired T-test or two-
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Question
1. One- versus Two-Sample T-Test For each scenario, choose paired T-test or two-sample T-test and justify your choice. a. The population of interest is all textbooks. We want to compare textbook prices in Bookstore A and B. Suppose we can afford a sample size of 100 from each bookstore. Two sample T-test: Randomly select 100 textbooks from Bookstore A and randomly select 100 textbooks from Bookstore B. After data collection (recording textbook prices), use the two-sample T-test to test for difference in means. Paired T-test: Randomly select 100 textbooks from Bookstore A and find the same textbooks from Bookstore B. After data collection (recording the difference in textbook prices in Bookstore A and B), use the paired T-test to compare mean diference. b. The population of interest is female gully cats. It is hypothesized that they are more aggressive when they are pregnant than when they are not pregnant. Suppose we can measure the aggressive level by a scale between 1 and 10. Two-sample T.test. Randomly select 7 cats without kittens and 7 cats with kittens (a total of 14 independent cats). After data collection (recording aggressive levels), use the two-sample T-test Paired T-test: Randomly select 7 cats without kittens. Compare the aggressiveness when they are with kittens. After data collection (recording the difference in aggressive levels before and after pregnancy), use the paired T-test.Explanation / Answer
Solution:
1.
a.
Conclusion:
In this given scenario, Paired T test seems to be more appropriate, as selecting different books from different stores can give an erroneous inference. Suppose all the books selected from Store A, maximum are costly ones. But this may not be same for store B, as most of the books selected from this store may be cheap.
Therefore, the appropriate test is Paired T test.
b.
Conclusion:
In the given scenario, Two sample T test is appropriate, as it will give proper estimate, because all cats behaviour is hypothesized.
c.
Conclusion:
In the given scenario, the two sample t test is more appropriate than paired t test. Evaluating which method is more appropriate can be analysed using 2 sample t test.
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