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Chapter 13: Problem 46

Suppose you give a random sample of students a questionnaire about extraversion, and some (10) are classified as extraverts and some (15) as not extraverts. You want to determine whether the typical GPA is higher for extraverts than for those who are not extraverts. Which test(s) can be used for each situation below? a. Both distributions are strongly skewed. b. Both distributions are nearly Normal. c. You have 100 extraverts and 150 who are not extraverts, and both distri- butions are skewed. Explain your choice of test.

Short Answer

Expert verified
For strongly skewed distributions, the Mann-Whitney U test can be used. For nearly normal distributions, the t-test is appropriate. For skewed distributions with a large sample size, the t-test can also apply due to the Central Limit Theorem.

Step by step solution

01

Situation A

For situation A where both distributions are strongly skewed, the appropriate test is the Mann-Whitney U test (also known as the Wilcoxon rank sum test). This non-parametric test does not make any assumptions about the distribution of the data and thus, is suitable for skewed distributions.
02

Situation B

When both distributions are nearly normal, it's best to use the t-test for comparing the means of two independent groups. The t-test assumes that the data is normally distributed and is used when the variance of the two groups are homoscedastic (i.e., they have the same variance).
03

Situation C

For the last situation where the sample size is large (100 extraverts and 150 non-extraverts) and both distributions are skewed, the Central Limit Theorem can be applied. According to this theorem, for large sample sizes the distribution of the sample means will be approximately normally distributed regardless of the shape of the population distribution. That being said, the t-test can again be used in this scenario because of the large sample size.

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