A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard. If the z-statistic is -2.58 and the level of significance is 0.02, what is your decision?
A) You reject the null hypothesis, and agree that less than 1% fail to meet government standards.
B) You have insufficient evidence to reject the null hypothesis.
C) You reject the alternate hypothesis and agree that less than 1% meet government standards.
D) You should have used the t-test.

Question

Quizplus · Accepted Answer

The z-statistic of -2.58 falls into the rejection region of the null hypothesis at a level of significance of 0.02. This means that the likelihood of obtaining a sample with ten or more products that do not meet the standard, assuming that less than 1% do not meet the standard, is less than 2%. Therefore, we reject the null hypothesis and agree with the manufacturer's claim that less than 1% of his products do not meet the minimum government standards. The t-test is not used in this scenario, as we have data on the population proportion and not the population mean.

A Manufacturer Claims That Less Than 1% of All His