23 A STAT 230 instructor is interested in whether there is a

23. A STAT 230 instructor is interested in whether there is any variation in the final exam grades between her two classes Data collected from the two classes are as follows: Section 1: n1 = 31, x, = 75, s1 = 12 Section 2: n2 = 30, x2 = 72, s2 = 14 Her null hypothesis and alternative hypothesis are: (a) Determine the test statistic. Show ail work: writing the correct test statistic, without supporting work, will receive no credit. (b) Determine the p-value for this test. Show ail work: writing the correct P-value. without supporting work will receive no credit. (C) Is there sufficient evidence to justify the rejection of H0 at the alpha=0.01 level? Explain.

Solution

(a) The test statistic is

F=s1^2/s2^2

=12^2/14^2

=0.73

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(b) It is a left-tailed test.

The degree of freedom df1=n1-1=31-1 = 30

The degree of freedom df2=n2-1=30-1 =29

So the p-value= P(F with df1=30 and df2=29 <0.73) = 0.1981 (from F table)

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(c) Since the p-value is larger than 0.01, we do not reject the null hypothesis.

So we can not conclude that there is sufficient evidence to justify the rejection of Ho.