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.

Answer 1

Answer:

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

Step-by-step explanation:

Complete Question is shown in the image below.

A scenario is presented in the statement and we need to describe what will be the Type 1 error in this case.

Remember that in Statistics Type 1 error means: Rejecting a true Null Hypothesis.

This means, if the test results favor the rejection of null hypothesis (and acceptance of alternate hypothesis), but in reality the null hypothesis is correct, then Type 1 error occurs in the study.

In simple words Type 1 error is the rejection of a true Null Hypothesis. The Null hypothesis in given case is:

The proportion of all washers produced with the specified diameter is equal to 90 percent.

And Alternate Hypothesis is:

The proportion of all washers produced with the specified diameter is greater than 90 percent.

Type 1 error in this case means: The test results reveal that Null hypothesis is to be rejected, i.e. rejection of the claim that proportion of washers is equal to 90% and accepting that proportion of washers is greater than 90%, but in reality the proportion of washers is equal to 90%.

Therefore, from the given options, the correct answer will be:

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