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 computed value of z = -2.25 and the level of significance is 0.03, 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

With a computed value of z = -2.25 and a level of significance of 0.03, we can find the corresponding critical value using a standard normal distribution table. The critical value is -2.17, which is less than -2.25. Since the computed value of z is in the rejection region, we reject the null hypothesis and conclude that there is sufficient evidence to support the manufacturer's claim that less than 1% of all the products do not meet the minimum government standards. The t-test would have been used if the population standard deviation was unknown or the sample size was less than 30. However, in this case, the normal distribution can be used because the sample size is large.

A Manufacturer Claims That Less Than 1% of All His