Machines at a factory produce circular washers with a specified diameter. The quality control manager at the factory periodicall

Question

2 days ago

7

Machines at a factory produce circular washers with a specified diameter. The quality control manager at the factory periodicall

y 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.

Mathematics

1 answer:

zzz [9K] · Answer 1 · 2026-03-25T19:09:07+03:00

Answer:

A Type I error could occur if the test shows that the proportion is above 90%, while in reality, the actual proportion is 90%.

Step-by-step explanation:

Machines in a factory produce circular washers that meet a specific diameter.

The quality control manager routinely assesses samples of washers to ensure that more than 90% conform to the specified diameter.

Let p represent the proportion of washers that meet the specified diameter

Thus, Null hypothesis: p = 90% $H_0$

Alternative Hypothesis: p > 90% $H_A$

Here, the null hypothesis posits that the proportion is exactly 90%. In contrast, the alternative hypothesis suggests that the proportion exceeds 90%.

Now, a Type I error indicates the probability of rejecting the null hypothesis while it is actually true or, in simple terms, the likelihood of incorrectly rejecting a valid hypothesis.

Thus, based on our question, a Type I error would declare that the test convincingly indicates the proportion is over 90%, while in truth, it remains 90%.