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Chapter 13: Problem 40

You know the grade point averages (GPAs) of a random sample of 10 full-time college students and 10 part-time college students. You want to test the hypothesis that the typical GPAs for full-time and part-time college students are different. Which test(s) should you choose for each situation? a. Suppose your preliminary investigation lead you to conclude that the distributions of GPAs for both groups are approximately Normal. b. Suppose your preliminary investigation lead you to conclude that the distributions of GPAs for both groups are not Normal but have the same shape.

Short Answer

Expert verified
For a Normal distribution, an independent samples t-test would be recommended, while for a non-Normal distribution with identical shape, the Mann-Whitney U test would be more appropriate.

Step by step solution

01

Analyze the distribution

For part (a), if preliminary investigation suggests that the distribution of GPAs for both full-time and part-time students follows a Normal distribution, use a t-test. This is because a t-test is most effective when the data follows a Normal distribution and our aim is to compare the means of two groups. Hence, the independent samples t-test is the appropriate choice.
02

Applicable test for normal distribution

In the case of normal distribution, apply the t-test which is designed to compare the means of the GPAs between the two independent groups. This involves finding the average GPA for each group and then seeing if the difference between those averages is statistically significant.
03

Analyze situation for non-Normal distribution

In part (b), if the distributions are not Normal but have the same shape, consider assuming heterogeneity of variance. Give Wilcoxon Rank Sum test a try where normality assumption is not required, also known as the Mann-Whitney U test. This test ranks the values from both sets of data from smallest to largest and then checks to see if one group tends to have higher or lower ranks than the other.
04

Applicable test for non-Normal distribution

In a non-Normal distribution scenario, non-parametric Mann-Whitney U test should be implemented. This test does not require the assumption of a Normal distribution and can be used even when the distributions are not the same. It essentially checks whether the distribution of the two samples are identical or not, without making any assumptions about the shape of the distribution.

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Most popular questions from this chapter

A professor tells his class that he knows their second exam score without their having to take the test. He tells them that the second exam score can be predicted from the first with this equation: Predicted second exam score \(=5+0.75\) (first exam score) This tells us that the deterministic part of the regression model that predicts second exam score on the basis of first exam score is a straight line. What factors might contribute to the random component? In other words, why might a student's score not fall exactly on this line?

A dean of students at a college wishes to estimate the typical future cumulative GPA for all first-year students who earned a \(2.0\) GPA during their first year. Should she use a prediction interval or a confidence interval? Why?

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