15. We wish to compare the variances of two populations. We take random samples

ID: 3135044 • Letter: 1

Question

from each with the following results:

Sample 1: n = 16, sample standard deviation = 9.9

Sample 2: n = 22, sample standard deviation = 6.6

a. What are the hypotheses for a 1-sided F test?

b. What is the F statistic for this test?

c. The critical value for a 1-sided F test based on these samples at ? = 0.10 is as shown

the graph below. Give the conclusion of this test at the 10% level.

(Assume an Anderson-Darling test fails to reject the null hypothesis of normality and we can

consider our F test results valid.)

Formulating the null and alternative hypotheses,

Ho:   sigma1^2 / sigma2^2   <=   1
Ha:    sigma1^2 / sigma2^2   >   1   [ANSWER]

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b)

As we can see, this is a    right   tailed test.
Getting the test statistic, as
s1 =    9.9
s2 =    6.6

Thus, F = s1^2/s2^2 =    2.25   [ANSWER]

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Thus, getting the critical F, as alpha =    0.1   ,
alpha =    0.1
df1 = n1 - 1 =    15
df2 = n2 - 1 =    21
F (crit) = 1.827

As F = 2.25 > 1.827, we reject Ho.

There is significant evidence at 0.10 level that the variance of population 1 is greater than the variance of population 2. [CONCLUSION]

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