One sample has SS - 48, and a second sample has SS - 32. If n - 5 for both sampl

Question

One sample has SS - 48, and a second sample has SS - 32. If n - 5 for both samples, And each of the sample variances and compute the pooled variance. Variance of first sample= Variance of second sample = Pooled variance = Because the samples are the same size, the pooled variance is: Exactly halfway between the two sample variances Closer to the second sample variance donor to the first sample variance Now assume that n - 5 for the first sample and n - 9 for the second. Again. calculate the two sample variances end the pooled valance. (If the pooled variance is not a whole number, use two demos places.)

Explanation / Answer

One sample has SS = 48 and

second sample has SS = 32

n=5 for both the sample.

variance of the first sample :

variance = SS / n-1 = 48 / 5-1 = 48/4 = 12

variance of the second sample = SS/ n-1 = 32 / 5-1 = 32/4 = 8

When sample sizes are equal then pooled variance is,

Sp2 = (variance of the first sample + variance of the second sample) / 2

= 12 + 8 / 2

= 20/2 = 10

Because samples are the same size the pooled variance is exactly halfway between the two sample variances.

Now assume that n = 5 for the first sample and n=9 for the second sample.

variance of the first sample :

variance = SS/n-1 = 48 / 5-1 = 48/4 = 12

variance of the second sample :

variance = SS/n-1 = 32 / 9-1 = 32/8 = 4

When sample sizes are not equal then pooled variance is,

Sp2 = [ (n1-1)*variance for one sample + (n2-1)*variance for second sample ] / n1+n2-2

= (5-1)*12 + (9-1)*4 / 5+9-2

= 4*12 + 8*4 / 12

= 6.67

The pooled variance is closer to the variance for the smaller sample.

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