Question

The mayor of a town has proposed a plan for the annexation of an adjoining community. A political study took a sample of 1000 voters in the town and found that 61% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 57%. Make the decision to reject or fail to reject the null hypothesis at the 0.10 level.

Answer 1

Solution :

This hypothesis test is a right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.57

H_a : p > 0.57

= 0.61

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.61 - 0.57 / [(0.57 * 0.43) / 1000]

= 2.555

P-value = 0.0053

= 0.10

P-value <

Reject the null hypothesis .