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Chapter 10: Q. 10.102 (page 431)

Suppose that the sample sizes, n4and n2, are equal for independent simple random samples from two populations.

a. Show that the values of the pooled and nonpooled r-statistics will be identical. (Hint: Refer to Exercise 10.61 on page 417.)

b. Explain why part (a) does not imply that the two t-tests are Equivalent (i.e., will necessarily lead to the same conclusion) when the sample sizes are equal.

Short Answer

Expert verified

a) The standard deviations for both are different.

b) The standard deviations for both are different.

Step by step solution

01

Part (a) Step 1: Given Information

To discover the proof that pooled and non-pooled t-test values are identical.

02

Part (a) Step 2: Explanation 

When the tests are run, it is discovered that the values for the pooled and non-pooled tests are not identical.

03

Part (b) Step 1: Given Information 

To ascertain the reason for the lack of equivalence.

04

Part (b) Step 2: Explanation 

Because the standard deviations for both tests differ, the tests do not have the same values for the same sample sizes.

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Most popular questions from this chapter

Define the phrase independent samples.

In each of Exercises 10.75-10.80, we have provided summary statistics for independent simple random samples from non populations. In each case, use the non pooledt-test and the non pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.

x~1=10,s1=2,n1=15,x~2=12,s2=5,n2=15

a. Two-tailed test伪=0.05.

b. 95%confidence interval.

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

In this Exercise, we have provided summary statistics for independent simple random samples from two populations. In each case, use the pooled t-lest and the pooledt-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.
x炉1=20,s1=4,n1=20,x炉2=24,s2=5,n2=15

a. Left-tailed test, 伪=0.05

b. 90%confidence interval

A variable of two population has a mean of 40and standard deviation of 12for one of the population and a mean of 40and a standard deviation of 6 for the other population.

a. For independent samples of sizes 9and4respectively find the mean and standard deviation of x1-x2

b. Must the variable under consideration be normally distributed on each of the two population for you to answer part (a) ? Explain your answer.

b. Can you conclude that the variable x1-x2is normally distributed? Explain your answer.
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