Question

he mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 10001000 voters in the town and found that 57% 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 above 53%. Make the decision to reject or fail to reject the null hypothesis at the 0.02 level.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.53

H_a : p > 0.53

= 0.57

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.57 - 0.53 / [(0.53 * 0.47) / 1000]

= 2.53

P(z > 2.53) = 1 - P(z < 2.53) = 0.0057

P-value = 0.0057

= 0.02

P-value <

Reject the null hypothesis .