Question

The mayor of a town has proposed a plan for the construction of a new bridge. A political study took a sample of 1400 voters in the town and found that 53% 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 50%. Make the decision to reject or fail to reject the null hypothesis at the 0.02 level.

Answer 1

Solution :

This hypothesis test is a right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.50

H_a : p > 0.50

= 0.53

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.53 - 0.50 / [(0.50 * 0.50) / 1400]

= 2.245

P-value = 0.0124

= 0.02

P-value <

Reject the null hypothesis .