A sample of 16 items from population 1 has a sample variance

A sample of 16 items from population 1 has a sample variance of 5.8 and a sample of 21 items from population 2 has a sample variance of 2.4. test the following hypotheses at the .05 level of significance.

Ho: less than or equal to

Ha: greater than

A. what is your conclusion using the p-value approach?

B. repeat the test using the critical value approach.

Solution

A. what is your conclusion using the p-value approach?

The test statistic is

F=s1^2/s2^2

=5.8/2.4

=2.42

It is a right-tailed test.

The degree of freedom df1=n1-1=16-1=15

The degree of freedom df2=n2-1=21-1=20

So the p-value= P(F with df1=15 and df2=20 >2.42) =0.0332 (from F table)

Since the p-value is less than 0.05, we reject the null hypothesis.

So we can conclude that the varaince for population 1 is greater than variance for population 2

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B. repeat the test using the critical value approach.

Given a=0.05, the critical value is F(0.95, df1=15, df2=20) =2.20 (from F table)

The rejection region is if F>2.2, we reject the null hypothesis

Since F=2.42 is larger than 2.20, we reject the null hypothesis.

So we can conclude that the varaince for population 1 is greater than variance for population 2