The producer of a certain bottling equipment claims that the variance of all their filled bottles is 0.027 or less. A sample of 30 bottles showed a standard deviation of 0.2. The p-value for the test is

Question

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The sample standard deviation is 0.2, which implies a sample variance of 0.04. Using a chi-square test for variance with 29 degrees of freedom, the calculated chi-square statistic is higher than expected under the null hypothesis, leading to a p-value between 0.025 and 0.05.

The Producer of a Certain Bottling Equipment Claims That the Variance