Chapter 10, Problem 7P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

As noted on page 283, when the two population means are equal the estimated standard error for the independent-measures *t* test provides a measure of how much difference to expect between two sample means. For each of the following situations, assume that
_{1} =
_{2} and calculate how much difference should be expected between the two sample means.

a. One sample has *n* = 6scores with *SS* **=** 75, and the second sample has n = 10 scores with *SS* = 135.

b. One sample has *n* = 6 scores with *SS* = 310, and the second sample has *n* = 10 scores with = 530.

c. In part b, the samples have larger variability (bigger SS values) than in part a, but the sample sizes are unchanged. How does larger variability affect the magnitude of the standard error for the sample mean difference?

**a.**

To determine

**To Find:** The measure of how much difference to expect between two sample means given

Explanation

**Given info:**

Two samples with size 6 and 10 have sum of squared difference (SS) equal 75 and 135 respectively. Also , when the two-population means are equal, the estimated standard error for the independent-measures t-test provides a measure of how much difference to expect between two sample means

**Calculations:**

The degrees of freedom for two samples is:

Similarly,

So, the pooled variance,

Substitute 75 for

**b.**

To determine

**To Find:** The measure of how much difference to expect between two sample means given

**c.**

To determine

**To Describe:** How does larger variability (larger SS) affect the estimated standard error.

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