Question summary: Is the variance in Division B ( \( S^2_B \) ) significantly different than the estimate for the pooled variance of all the divisions ( \( \sigma^2 \) )?
When I first attempted part iii)c), I used the F distribution to compare the two variances.
The \( H_0 \) I chose was that \( S^2_B = \sigma^2 \).
Under \( H_0 \), I assume the variance of Division B is the same as the overall variance, hence I ended up with \( \frac{S^2_B}{\sigma^2} \) as my test statistic. However, the answer uses the chi-square test. I understand why the chi-square test is used, using \( H_0 \) : \( S^2_B \) = 3.87.
My question is: Is the reason the F-test cannot be used because technically \( S^2_B \) and \( \sigma^2 \) are not independent because \( \sigma^2 \) is calculated using data from Division B?
Thanks. =)
Last edited by a moderator: Oct 1, 2016
