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: $H_0:p\leq0.53$

$H_a:p>0.53$

Step-by-step 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 :

$H_0:p\leq0.53$

$H_a:p>0.53$