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 -1.96 and the level of significance is 0.01, what is your decision?
A) You reject the null hypothesis.
B) You have insufficient evidence to reject the null hypothesis.
C) You accept 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 null hypothesis is that the proportion of products not meeting the standard is equal to or greater than 1%, and the alternate hypothesis is that the proportion is less than 1%. We can use a one-tailed z-test for proportions to test this.

The calculated z-statistic (-1.96) falls in the rejection region (left tail) at a level of significance of 0.01. However, we need to compare this to the critical value of the z-distribution, which is -2.33 for a one-tailed test at a 0.01 level of significance with a sample size of 500. Since our calculated z-statistic (-1.96) is greater than the critical value (-2.33), we have insufficient evidence to reject the null hypothesis. Therefore, we conclude that there is no significant evidence to suggest that the proportion of products not meeting the standard is less than 1%.

A Manufacturer Claims That Less Than 1% of All His