Question

Machines at a factory produce circular washers with a specified diameter. The quality control manager at the factory periodically tests a random sample of washers to be sure that greater than 90 percent of the washers are produced with the specified diameter. The null hypothesis of the test is that the proportion of all washers produced with the specified diameter is equal to 90 percent. The alternative hypothesis is that the proportion of all washers produced with the specified diameter is greater than 90 percent.

Which of the following describes a Type I error that could result from the test?

A) The test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%.

B) The test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%.

C) The test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%.

D) The test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%.

E) A Type I error is not possible for this hypothesis test.

Answer 1

The Type I error that could result from the test is that The test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%.

Explanation:

We are given that machines at a factory produce circular washers with a specified diameter.

The quality control manager at the factory periodically tests a random sample of washers to be sure that greater than 90 percent of the washers are produced with the specified diameter.

Let p = proportion of all washers produced with the specified diameter

So, Null hypothesis,
`H_0` : p = 90%

Alternate Hypothesis,
`H_A` : p > 90%

Here, null hypothesis states that the proportion of all washers produced with the specified diameter is equal to 90%.

On the other hand, alternate hypothesis states that the proportion of all washers produced with the specified diameter is greater than 90%.

Now, Type I error states the Probability of rejecting null hypothesis given the fact that null hypothesis was true or in other words Probability of rejecting a true hypothesis.

So, according to our question Type I error would be that the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%.