Question

The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 1300 voters in the town and found that 60% 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 less than 63%. Testing at the 0.01 level, is there enough evidence to support the strategist's claim? Step 6 of 7: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Solution :

The null and alternative hypothesis is

H0 : p = 0.63

Ha : p < 0.63

= 0.60

P0 = 0.63

1 - P0 = 0.37

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.60 - 0.63 / [(0.63 * 0.37) / 1300]

z = -2.24

P-value = 0.0125

= 0.01

P-value >

Fail to reject the null hypothesis .

There is no sufficient evidence to support the claim.