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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

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.

  1. a. Each sample has n = 4 stores with s2 = 68 for the first sample and s2 = 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 s2 = 68 for the first sample and s2 = 76 for the second.
  3. 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, sp2 , is the average of the two variances That is,

sp2=s12+s222=68+762=1442=72

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

sM1M2=sp

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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