Question

An instructor at a major research university occasionally teaches summer session and notices that that there are often students repeating the class. Out of curiosity, she designs a random sample of students enrolled in summer sessions and counts the number repeating a class. She counts 105 students in the sample, of which 19 are repeating the class.She hypothesizes that, in general, 10% of students repeat a course. The hypotheses to be tested are:

a) H0:p? =0.181 vs. H?:p=0.1 .
b) H0:p=0.1 vs. H?:p?0.18 .
c) H0:p=0.1 vs. H?:p? =0.181 .
d) H0:p=0.1 vs. H?:p?0.1 .

Answer 1

We want to test the the claim that in general, 10% of students repeat a course and thats what we want to verify so then the system of hypothesis are:

Null hypothesis:
`p =0.1`

Alternative hypothesis
`p \\eq 0.1`

And the best option for this case is given:

d) H0:p=0.1 vs. H1:p
`\\eq` 0.1

Explanation:

For this case we have the folloing info:

`X= 19` number of people repeating the class

`n =105` the sampel size selected

`\hat p =(19)/(105)=0.181` the estimated proportion of people repeating the class

We want to test the the claim that in general, 10% of students repeat a course and thats what we want to verify so then the system of hypothesis are:

Null hypothesis:
`p =0.1`

Alternative hypothesis
`p \\eq 0.1`

And the best option for this case is given:

d) H0:p=0.1 vs. H1:p
`\\eq` 0.1 .