A PC Company Uses Two Suppliers for Rechargeable Batteries for Its

Question

Examlex · Accepted Answer

The Answer is Ideally, we would like to test whether the two population standard deviations are equal.
However, there is no test available for doing this test directly. Instead, we must convert to variances and
perform the F-test. The following null and alternative hypotheses would be appropriate in this situation:

Ideally, we would like to test whether the two population standard deviations are equal. However, there is no test available for doing this test directly. Instead, we must convert to variances and perform the F-test. The following null and alternative hypotheses would be appropriate in this situation: This will be a two-tailed test since we are testing to see whether a difference exists and are not predicting which battery will have more or less variability. In a two-tailed test of variances, the test statistic is an F- value that is formed by the ratio of the two sample variances and by placing the larger sample variance in the numerator: We then compare this value to a critical value from the F-distribution table. Since this is a two-tailed test with alpha = 0.10, we use the table with 0.05 in the upper-tail of the F-distribution. Two sets of degrees of freedom are used with the F-distribution. Across the top of the F-table we look for degrees of freedom corresponding to n-1 where n is the sample size associated with the sample variance that was placed in the numerator of the F-test statistic. In our case, n = 9, so the degrees of freedom is 9 - 1 = 8 for the numerator. The degrees of freedom down the side in the F-table is n-1 where n corresponds to the sample size for the sample variance in the denominator of the F-test statistic. In our case, that would be n = 12. Thus, the denominator degrees of freedom are 12 - 1 = 11. Then the critical F from the 0.05 table with 8 and 11 degrees of freedom is 2.948. The decision rule is: If F calculated > 2.948 reject H0, otherwise do not reject. Since our calculated F-test statistic is F = 1.2799 < 2.948, we do not reject the null hypothesis. Thus, based on the sample information, we have no basis for believing that there is a difference in the two batteries with respect to variability in use time.

This will be a two-tailed test since we are testing to see whether a difference exists and are not predicting
which battery will have more or less variability. In a two-tailed test of variances, the test statistic is an F-
value that is formed by the ratio of the two sample variances and by placing the larger sample variance in
the numerator:

We then compare this value to a critical value from the F-distribution table. Since this is a two-tailed test
with alpha = 0.10, we use the table with 0.05 in the upper-tail of the F-distribution.
Two sets of degrees of freedom are used with the F-distribution. Across the top of the F-table we look for
degrees of freedom corresponding to n-1 where n is the sample size associated with the sample variance
that was placed in the numerator of the F-test statistic. In our case, n = 9, so the degrees of freedom is 9 - 1
= 8 for the numerator. The degrees of freedom down the side in the F-table is n-1 where n corresponds to
the sample size for the sample variance in the denominator of the F-test statistic. In our case, that would
be n = 12. Thus, the denominator degrees of freedom are 12 - 1 = 11. Then the critical F from the 0.05 table
with 8 and 11 degrees of freedom is 2.948. The decision rule is:
If F calculated > 2.948 reject H0, otherwise do not reject.
Since our calculated F-test statistic is F = 1.2799 < 2.948, we do not reject the null hypothesis. Thus, based
on the sample information, we have no basis for believing that there is a difference in the two batteries
with respect to variability in use time.

A PC Company Uses Two Suppliers for Rechargeable Batteries for Its

Definitions: