The producer of a certain bottling equipment claims that the variance of all its filled bottles is .027 or less. A sample of 30 bottles showed a standard deviation of .2. The p-value for the test is _____.
A) between .025 and .05
B) between .05 and .01
C) .05
D) .025

Question

Quizplus · Accepted Answer

The p-value indicates the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct. In this case, the null hypothesis would be that the variance is .027 or less. Given the sample size of 30 and a sample standard deviation of .2, which is significantly higher than the claimed variance, the p-value would likely indicate that it is relatively unlikely to observe such a deviation if the true variance were indeed .027 or less. The option "between .025 and .05" suggests a low but not extremely low probability, fitting the scenario where the observed data somewhat strongly contradicts the claim, but not to an extreme extent.

The Producer of a Certain Bottling Equipment Claims That the Variance