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Chapter 10: Q.10.101 (page 430)

Refer again to Fig. 10.8 on page 427, where each pair of graphs shows the distributions of a variable on two populations. Suppose that, in each case, you want to perform a small-sample hypothesis test based on independent simple random samples to compare the means of the two populations. In each case, decide which, if any, of the following tests is preferable: the pooled t-test, the non pooled t-test, or the Mann-Whitney test. Explain your answers.

Short Answer

Expert verified
  1. We will prefer the pooled test procedure.
  2. Non pooled test procedure will be prefer.
  3. We will prefer Man-Whitney test
  4. We will not prefer Man-Whitney test

Step by step solution

01

Given Information 

Given in the question that, refer figure 10.8

We have to decide which, if any, of the following tests is preferable: the pooled t-test, the non pooled t-test, or the Mann-Whitney test. Explain your answers.

02

Part (a) Step 2: Explanation 

Consider the given figure.

The two standard deviation values are close in the given figure (a), and the two distributions are normal. As a result, pooled testing is preferred.

03

Part (b) Step 1: Given information 

Consider the given figure (b)

04

Part (b) Step 2: Explanation 

The two standard deviation values are not similar in figure 10.8 (b), and the two distributions are not normal. As a result, non pooled testing is favored.

05

Part (c) Step 1: Given Information 

Consider the given figure (c)

06

Part (c) Step 2: Explanation

Figure 10.8 (c) shows that the two distributions are not normal and do not have the same shape. The Mann-Whitney test method assumption is met. Thus, the Man-Whitney test is recommended.

07

Part (d) Step 1: Given Information 

Given in the question that,

08

Part (d) Step 2: Explanation 

The two distributions are not normal and do not have the same shape, as seen in figure 10.8 (d). The Mann-Whitney test procedure's assumption is not met. As a result, the Man-Whitney test is not recommended.

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Most popular questions from this chapter

You know that the population standard deviations are equal.

H2:渭1<渭2

The primary concern is deciding whether the mean of Population 1 differs from the mean of Population 2 .

In each of Exercises 10.35-10.38, we have provided summary statistics for independent simple random samples from two populations. Preliminary data analyses indicate that the variable under consideration is normally distributed on each population. Decide, in each case, whether use of the pooled t-lest and pooled t-interval procedure is reasonable. Explain your answer.
10.37 x炉1=118,s1=12.04,n1=99
x2=110,s2=11.25,n2=80

In each of Exercises 10.35-10.38, we have provided summary statistics for independent simple random samples from two populations. Preliminary data analyses indicate that the variable under consideration is normally distributed on each population. Decide, in each case, whether use of the pooled t-lest and pooled t-interval procedure is reasonable. Explain your answer.
10.35 x炉1=468.3,s1=38.2,n1=6

x2=394.6,s2=84.7,n2=14
See all solutions

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