Hypothesis testing
posted by Moe
5 Part Question:
6 timed runs were made along route A with an average of 95 minutes and a standard deviation of 10.5 minutes. Route B had 8 test runs with an average of 93 minutes and a standard deviation of 5.2 minutes. Determine if there sufficient evidence that route B is more consistent with 95% confidence.
Part 1: Which test is used?
F, Studentt, Chisquare, Normal
(I'm pretty sure this is a "t" test)
Part 2: What is the critical test value?
4.88, 3.58, 3.97, 4.08
(This is where I need the help,I'm not
getting anywhere close to these)
Part 3: What is the calculated value?
4.88, 3.58, 3.97, 4.08
(same situation as above)
Part 4: Is this a onetail test or two?
(I'm fairly sure this is a two tail
because the question is looking for
any change at all...hi or low)
Part 5: Do we reject the null hypothesis
Fail to reject
Reject (route B is more consistent)
Thanks for any help you can give!

DQR
Actually, it's not a ttest. The question doesn't ask whether the route is shorter or longer, but whether the route is more consistent  and that means whether its less variable. To find THAT out, you need to ask whether the standard deviation for Route B is significantly smaller than the standard deviation for Route A.
You can do that with an F test on the two variances (i.e. the squares of the standard deviations), by dividing the Route A variance by the Route B variance (note that this is a ONEtailed test, because you're only considering the possibility that B is more consistent than A, not whether there's any difference at all). The test statistic (i.e. the calculated value) is therefore (10.5)^2 / (5.2)^2 = 4.08. Aha! It looks as though we're on the right track, because that's Part 3 answer (d).
But we've skipped Part 2: what's the critical test value? We need a set of F tables to answer that one, namely the 95% cutoff value for an F statistic on (N11) and (N22) degrees of freedom. N1 = 6, and N2 = 8. But I think perhaps its time you took over now... 
Joe
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