A manufacturer wants to know if the variance of their product is 84 if a sample of 28 had a variance of 79. Test the claim at the .05 level.

State the hypotheses and identify the claim, find the critical value(s), compute the test value, and make the decision, summarize the results.

Solution: We need to test the following hypotheses:

We use a two tailed test Chi-Square test. The critical values for this test, withand 27 degrees of freedom are

The rejection region is given by

We compute now the

Chi Square
statistics:

Sincedoesn’t fall on the rejection are, we fail to reject the null hypothesis. This means that the sample doesn’t provide enough information to reject the claim, at the 0.05 significance level.

This means that we reject the null hypothesis. In other words, we have enough evidence to support the claim that there’s a difference with the new coating, at the 0.01 significance level.

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