   Chapter 10, Problem 5P Essentials of Statistics for the B...

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

Solutions

Chapter
Section Essentials of Statistics for the B...

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

One sample has SS = 36 and a second sample has SS = 18.a. If n = 4 for both samples, find each of the sample variances and compute 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 = 4 for the first sample and n = 7 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 sample.

a.

To determine

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

Explanation

Given info:

Two samples each of size 4 has sum of squared difference (SS) equal 36 and 18.

Calculations:

The formula for sample variance is:

s2=SSn1

Substitute SS1=36 and n1=4.

s12=363=12

Similarly, substitute SS2=18 and n2=4

s22=183=6

Now, the degrees of freedom 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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