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Chapter 10: Q. 2 (page 445)

Discuss the basic strategy for comparing the means of two populations based on a simple random paired sample.

Short Answer

Expert verified

The following advancements outline the basic technique for examining the methods for two populations of paired sample based on free basic irregular examples:

1. Select an example from the matched sample independently and arbitrarily.

2. Analyze the difference between the matched values of the variable under investigation.

3. Remove an unneeded source of variance with a paired sample.

4. As a result of the checking blunder made in assessing the impact between the populaces means, the effect between the populaces means will typically be less and, in this manner, obligated to differentiate distinction between the people indicates when such references exist.

Step by step solution

01

Given Information

To go through the basics of using an independent simple random paired sample to compare the means of two populations.

02

Explanation

Assume that for the paired sample, xis a regularly distributed variable.

The difference between the values of the variable Xon the members of the pair designated by dis called the paired difference variable and is calculated for each pair.

渭d=渭1-渭2

The random variable for the paired sample is normally distributed.

Test statistics:

When the population standard deviations are known, compare two population means.

z=x1炉-x2炉-渭1-渭2c1n12+c2m22

In a paired sample of size n, compare two population means as follows:

t=d炉-渭dsdn~t(n-1)

Where sdis the standard deviation

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Most popular questions from this chapter

A variable of two populations has a mean of 7.9and a standard deviation of 5.4for one of the populations and a mean of 7.1and a standard deviation of 4.6for the other population. Moreover. the variable is normally distributed in each of the two populations.

a. For independent samples of sizes 3and 6, respectively, determine the mean and standard deviation of x1-x2.

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

c. Determine the percentage of all pairs of independent samples of sizes 4and 16, respectively, from the two populations with the property that the differencex1-x2 between the simple means is between -3and 4.

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

x炉1=20,s1=4,n1=10,x炉2=18,s2=5,n2=15

a. Right-tailed test,伪=0.05

b. 90%confidence interval

Recess and Wasted Food. Refer to Exercise 10.50 and find a 98% confidence interval for the difference between the mean amount of food wasted for lunches before recess and that for lunches after recess.

In this section, we introduced the pooled t-test, which provides a method for comparing two population means. In deriving the pooled f-test, we stated that the variable

z=f^1-x^2-渭1-渭2蟽1/n1+1/n2

cannot be used as a basis for the required test statistic because 蟽 is unknown. Why can't that variable be used as a basis for the required test statistic?

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 of the variable under consideration have the same shape, but are not normal, and both sample sizes are large. 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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