Question

The mayor of a town has proposed a plan for the construction of a new bridge. A political study took a sample of 1200 voters in the town and found that 56% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 53%. State the null and alternative hypotheses.

Answer 1

Answer:
`H_0:p\leq0.53`

`H_a:p>0.53`

Explanation:

Claim : A a political strategist wants to test the claim that the percentage of residents who favor construction is more than 53%.

Let 'p' be the percentage of residents who favor construction .

Claim :
`p> 0.53`

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\leq0.53`

And the alternative hypothesis must be :-

`H_a:p>0.53`

Thus, the null hypothesis and the alternative hypothesis for this test :

`H_0:p\leq0.53`

`H_a:p>0.53`