Question

A college instructor claims that the proportion of students who will fail the final exam is less than 10%.     To test this claim, a random sample of student results on the final exam is monitored.

Assume that the test statistic for this hypothesis test is −2.13.

Assume the critical value for this hypothesis test is −1.645.

Come to a decision for the hypothesis test and interpret your results with respect to the original claim.

Select the correct answer below:

a) Fail to reject the null hypothesis.
There is not enough evidence to support the claim that the proportion of students who will fail the final exam is less than 10%.

b) Reject the null hypothesis.
There is enough evidence to support the claim that the proportion of students who will fail the final exam is less than 10%.

Answer 1

Solution:
Given in the question College instructor claims that the proportion of students who will fail the final exam is less than 10% So we can write null and alternate hypothesis as follows:
Null hypothesis H0: p= 0.10
Alternate hypothesis Ha: p < 0.10
Also Given Test statistic Value = -2.13
Critical value = -1.645
As this is one tailed and left tailed analysis so decision rule, If the test statistic value is less than -1.645 so we will reject the null hypothesis.
Here we can see that test statistic value is less than -1.645 i.e. (-2.13<-1.645) so we can reject the null hypothesis and we have significant evidence to support the claim that the proportion of students who will fail the exam is less than 10%.