One sample has SS = 46 and a second sample has SS = 40. (a) Assuming that n = 8
ID: 3150113 • Letter: O
Question
One sample has SS = 46 and a second sample has SS = 40.
(a) Assuming that n = 8 for both samples, calculate each of the sample variances, then 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. (Use 2 decimal places.)
pooled variance
(b) Now assume that n = 8 for the first sample and n = 17 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. (Use 2 decimal places.)
pooled variance
Explanation / Answer
a)
Note that
Var(x) = s^2 = SS/(n-1)
Hence,
FIRST SAMPLE: s1^2 = 46/(8-1) = 6.571428571 [ANSWER, VARIANCE]
SECOND SAMPLE: s2^2 = 40/(8-1) = 5.714285714 [ANSWER, VARIANCE]
Calculating the standard deviations of each group,
s1 = 2.563479778
s2 = 2.390457219
Thus, the pooled standard deviation is given by
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]
As n1 = 8 , n2 = 8
Then
S = 2.478478796
Hence,
S^2 = pooled variance = 6.142857142 [ANSWER, POOLED VARIANCE]
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b)
Note that
Var(x) = s^2 = SS/(n-1)
Hence,
FIRST SAMPLE: s1^2 = 46/(8-1) = 6.571428571 [ANSWER, VARIANCE]
SECOND SAMPLE: s2^2 = 40/(17-1) = 2.5 [ANSWER, VARIANCE]
Calculating the standard deviations of each group,
s1 = 2.563479778
s2 = 1.58113883
Thus, the pooled standard deviation is given by
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]
As n1 = 8 , n2 = 17
Then
S = 1.933683127
Hence, the pooled variance is
S^2 = 1.933683127^2 = 3.739130436 [ANSWER]
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