One sample has SS=60 and a second sample has SS=48. A. if n=7 for both samples,
ID: 3362401 • Letter: O
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 largest sample.
Explanation / Answer
for first case 12=60 and s22=48, n1=7 and n2=7
pooled variance sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2
sp2 is average of 60 and 48 i.e.(60+48)/2=54
for second case 12=60 and s22=48, n1=7 and n2=5
pooled variance sp2 is the weight average of s12 and s22, so larger sample weight will be more and pooled variance is closer to the variance for the largest sample.
si2 ni (ni-1)si2 60 7 360 48 7 288 108 14 648 sp2=648/12= 54Related Questions
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