One sample has SS = 60 and a second sample has SS = 48. a. If n = 7 for both sam

Question

One sample has SS = 60 and a second sample has SS = 48.

a.         If n = 7 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 = 7 for the first sample and n = 5 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.

Explanation / Answer

a) first sample variance =SS1/(n1=1) =60/(7-1) =10

and second sample variance =SS2/(n2-1) =48/(7-1) =8

pooled variance =(SS1+SS2)/(n1+n2-2) = (60+48)/(7+7-2) =9

b)

first sample variance =SS1/(n1=1) =60/(7-1) =10

and second sample variance =SS2/(n2-1) =48/(5-1) =12

pooled variance =(SS1+SS2)/(n1+n2-2) = (60+48)/(7+5-2) =10.8

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