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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

One sample has SS = 70 and a second sample has SS = 42.

a. If n = 8 for both samples, find each of the sample variances, and calculate the pooled variance. Because the samples are the same size, you should find that the pooled variance is exactly halfway between the two sample variances.

b. Now assume that n = 8 for the first sample and n = 4 for the second. Again, calculate the two sample variances and the pooled variance. You should find that the pooled variance is closer to the variance for the larger simple.

a.

To determine

To Find: The samplevariances and pooled variance for the given question

Explanation

Given info:

Two samples each with size 8 have sum of squared difference (SS) equal 70 and 42 respectively.

Calculations:

The formula for sample variance is:

s2=SSn1

Substitute SS1=70 and n1=8 to get s12

s12=707=10

Similarly, substitute values SS2=42 and n2=8 to get s22

s22=427=6

Now, the degrees of freedom for two samples are calculated as:

df1=df2=n1

b.

To determine

To Find: The sample variances and pooled variance for the given question.

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