1. Chapter 10, Problem 5 One sample has SS- 48, and a second sample has SS-32 If

Question

1. Chapter 10, Problem 5 One sample has SS- 48, and a second sample has SS-32 If n = 5 for both samples, find 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: O Closer to the first sample variance O Exactly halfway between the two sample variances O Closer to the second sample variance Now assume that n = 5 for the first sample and n = 9 for the second. Again, calculate the two sample variances and the pooled variance. (If the pooled variance is not a whole number, use two decimal places.) Variance of first sample Variance of second sample Pooled variance The pooled variance is: O Closer to the variance for the smaller sample O Closer to the variance for the larger sample O Exactly halfway between the two sample variances

Explanation / Answer

First sample SS1 =48

Second sample SS2 =32

n= 5

Sample variance for the first sample,= SS1/(n-1)=48/5-1=48/4=12

Sample variance for the second sample,= SS2/(n-1)=32/(5-1)=32/4=8

The pooled variance,Sp2= [(n-1)s12 + (n2-1)s22] / (n1+n2-2) = [48 + 32] / (5+5-2) = 80/8 =10

The pooled variance is 10

Here we observe that: Because the samples are the same size, the pooled variance is Exactly halfway between the two sample variances

B. n1 = 5 for the first sample

n2 = 9 for the second sample.

The sample variance for the first sample= SS1/(n1-1)=48/(5-1)=48/4=12

The sample variance for the second sample = SS2/(n2-1)=32/(9-1)=32/8=4

The pooled variance, Sp2= [(n1-1)s12+(n2-1)s22] / (n1+n2-2)=[48+32] / (5+9-2)= 80/12= 6.67

So we see that the pooled variance is closer to the variance of the larger sample.

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