Question

Tristan is an administrator for a private nonprofit college and read a surprising statistic that 74% of graduates from private nonprofit colleges in the region had at least one outstanding student loan at the time of graduation. He believes that percentage is high and claims that the proportion of graduates at his college is less than the regional rate. Tristan randomly selects 135 graduates from his college and finds that 92 had at least one outstanding student loan at the time of graduation. What are the null and alternative hypotheses for this hypothesis test?

Answer 1

Answer:
`H_0: p=0.74\\\\ H_a:p<0.74`

Explanation:

Let p be the population proportion for the graduates from private nonprofit colleges in the region had at least one outstanding student loan at the time of graduation.

Given : Tristan is an administrator for a private nonprofit college and read a surprising statistic that 74% of graduates from private nonprofit colleges in the region had at least one outstanding student loan at the time of graduation.

i.e.
`p=0.74`

He believes that percentage is high and claims that the proportion of graduates at his college is less than the regional rate.

i.e.
`p<0.74`

Since, the null hypothesis is a statement which always takes equal sign or generally shows " no difference " where as alternative hypothesis takes unequal signs.

Then, the null and alternative hypotheses for this hypothesis test :-

`H_0: p=0.74\\\\ H_a:p<0.74`