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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


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 pooled t-test and the non pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.

x¯1=15,s1=2,n1=15,x¯2=12,s2=5andn2=15.

a. Two-tailed test, α=0.05

b. 95%confidence interval.

H2:μ1>μ2

O. Ehimwenma and M. Tagbo, researchers in Nigeria, were interested in how the characteristics of the spleen of residents in their tropical environment compare to those found elsewhere in the world. They published their findings in the article "Determination of Normal Dimensions of the Spleen by Ultrasound in an Endemic Tropical Environment" (Nigerian Medical Journal, Vol. 52, No. 3, pp. 198-203). The researchers randomly sampled 91males and 109females in Nigeria. The mean and standard deviation of the spleen lengths for the males were 11.1cmand 0.9cmrespectively, and those for the females were 10.1cmand 0.7cm, respectively. At the1% significance level, do the data provide sufficient evidence to conclude that a difference exists in mean spleen lengths of male and female Nigerians?

Driving Distances. Refer to Exercise 10.48 and determine a 95% confidence interval for the difference between last year's mean VMTs by midwestern and southern households.

Suppose that you want to perform a hypothesis test to compare the means of two populations, using independent simple random samples. Assume that the two distributions (one for each population) of the variable under consideration are normally distributed and have equal standard deviations. Answer the following questions and explain your answers.

a. Is it permissible to use the pooled t-test to perform the hypothesis test?

b. Is it permissible to use the Mann-Whitney test to perform the hypothesis test?

c. Which procedure is preferable, the pooled t-test or the Mann-Whitney test?
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