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Essentials of Statistics for the B...

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

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Section
BuyFindarrow_forward

Essentials of Statistics for the B...

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 μ 1 = μ 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 μ1=μ2 (i.e. calculateestimated standard error).

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:

df1=n11=61=5

Similarly,

df2=n21=101=9

So, the pooled variance, sp2, is calculated using formula:

sp2=SS1+SS2df1+df2

Substitute 75 for SS1, 135 for SS2, 5 for df1 and 9 for df2 in the above fo

b.

To determine

To Find: The measure of how much difference to expect between two sample means given μ1=μ2 (i.e. calculate estimated standard error).

c.

To determine

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

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