Question

A decade-old study found that the proportion of high school seniors who felt that "getting rich" was an important personal goal was 72% . Suppose that we have reason to believe that this proportion has changed, and we wish to carry out a hypothesis test to see if our belief can be supported. State the null hypothesis and the alternative hypothesis that we would use for this test.

Answer 1

Answer:
`H_0:p\leq0.72`

`H_a:p\\eq0.72`

Explanation:

Given : A decade-old study found that the proportion of high school seniors who felt that "getting rich" was an important personal goal was 72% .

Let 'p' be the new proportion of high school seniors who felt that "getting rich" was an important personal goal .

Claim :
`p\\eq0.72`

We know that the null hypothesis has equal sign.

Therefore , the null hypothesis for the given situation will be opposite to the given claim will be :-

`H_0:p=0.72`

And the alternative hypothesis must be :-

`H_a:p\\eq0.72`

Hence, the null hypothesis and the alternative hypothesis that we would use for this test :

`H_0:p\leq0.72`

`H_a:p\\eq0.72`