Question

The mayor of a town has proposed a plan for the annexation of an adjoining community. A political study took a sample of 1400 voters in the town and found that 75% 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 over 72%. 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 = 0.72

H_a : p > 0.72

= 0.75

n = 1400

P₀ = 0.72

1 - P₀ = 1 - 0.72

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.75 - 0.72 / [(0.72 * 0.38 / 1400]

= 2.15

P(z > 2.15) = 1 - P(z < 2.15) = 0.01136

P-value = 0.01136

= 0.2

P-value <

Reject the null hypothesis .