Chapter 10, Problem 11P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

For each of the following, assume that the two samples are obtained from populations with the same mean, and calculate how much difference should be expected, on average, between the two sample means.

- a. Each sample has n = 4 stores with
*s*^{2}= 68 for the first sample and*s*= 76 for the second (Note: Because the two samples are the same size, the pooled variance is equal to the average of the two sample variances.)^{2} - b. Each sample has n = 16 scores with
*s*= 68 for the first sample and^{2}*s*= 76 for the second.^{2} - c. In Part b, the two samples are bigger than in Part a, but the variances are unchanged. How docs sample size affect the size of the standard error for the sample mean difference?

**a.**

To determine

**To Find:** The difference to expect, on average, between two sample means (That is, calculate estimated standard error).

Explanation

**Given info:**

Two samples each with size 4 have variance 68 and 76 respectively.

**Calculations:**

Since the two samples are of same size, the pooled variance,

Now, the formula for estimated standard error of the difference is,

**b.**

To determine

**To Find:** The difference to expect, on average, between two sample means (That is, calculate estimated standard error).

**c.**

To determine

**To Describe:** How does larger sample size affect the estimated standard error.

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