Question

The mayor of a town has proposed a plan for the construction of a new bridge. A political study took a sample of 800 voters in the town and found that 67% 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 over 63%. Make the decision to reject or fail to reject the null hypothesis at the 0.05 level.

Answer 1

We have to reject null hypothesis

Explanation:

n = 800

P* = sample proportion = 0.67

Alpha = 0.05

Null hypothesis h0: proportion = 63%

Alternate hypothesis h1: proportion > 64%

Test statistics:

Z = (p* - P)/√pq/n

Z = 0.67 - 0.64/√0.63x0.37/800

= 0.67 - 0.63/0.017

=0.04/0.017

= 2.352

At 0.05 the critical value of z = 1.645

We compare z calculated and z critical value.

2.352 is greater than 1.645 therefore we take the decision to reject the null hypothesis at 0.05 level of significance.

The percentage of residents that supports construction is greater than 63%