At a manufacturing company, the percent of defective items produced on the assembly line is 2%. The company is testing a new assembly line designed to reduce the percent of defective parts. The
null and alternative hypotheses of the test are described as follows.
H : The percent of defective parts is at least 2%.
H : The percent of defective parts is less than 2%.
Which of the following describes a Type II error that could result from the test?
A) The test does not provide convincing evidence that the percent is less than 2%, but the actual percent is 3%.
Submit
B
The test does not provide convincing evidence that the percent is less than 2%, but the actual percent is 2%
C) The test does not provide convincing evidence that the percent is less than 2%, but the actual percent is 1%.
D
The test provides convincing evidence that the percent is less than 2%, but the actual percent is 2%
E
The test provides convincing evidence that the percent is less than 2%, but the actual percent is 1%.

A Type II error occurs if a false null hypothesis is not rejected. In this case, the new assembly line does reduce the percent of defective items, but the test fails to detect it.

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astha8579 astha8579 · Answer 2 · 2022-01-28T10:49:18+01:00

You can use the definition of type II error to identify what option describes a Type II error.

The option that describes a type II error that could result from the test is:

Option C) The test does not provide convincing evidence that the percent is less than 2% (ie we cannot reject null hypothesis and thus accept it), but the actual percent is 1% (ie the accepted null hypothesis was wrong in reality, thus, causing type II error)

What is Type I and Type II error?

Firstly the whole story starts from hypotheses. The null hypothesis is tried to reject and we try to accept the alternate hypothesis.

The type 1 error occurs if we get false positive conclusion (false positive means we accuse null hypothesis being wrong when it was actually correct).
The type 2 error occurs if we get false negative conclusion (false negative means we accept null hypothesis when it was actually false).

The negative is just like the doctor's test getting negative means no disease. Similarly, if we conclude null hypothesis negative means it is accepted. If it is accepted wrongly means the negative test result was false, thus called false negative. This error is called type II error.

What is type II error in given context?

Since the specified null hypothesis is [tex]H_0[/tex] = The percent of defective parts is at least 2%.

Thus, according to the aforesaid definition of type II error, we get:
Acceptance of null hypothesis since the test doesn't provide enough evidence for alternate hypothesis to be true or that the test doesn't provide enough evidence that the percent is less than 2% but the actual percent is less than 2%

Thus, Option C) The test does not provide convincing evidence that the percent is less than 2%(ie we cannot reject null hypothesis and thus accept it), but the actual percent is 1%(ie the accepted null hypothesis was wrong in reality, thus, causing type II error)

Learn more about type I and type II error here:

https://brainly.com/question/26067196