Question

The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 1200 voters in the town and found that 76% 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 73%. Make the decision to reject or fail to reject the null hypothesis at the 0.10 level.

Answer 1

Solution :

Given that,

= 0.73

1 - = 0.27

n = 1200

Level of significance = = 0.10

Point estimate = sample proportion = = 0.76

This a right (One) tailed test.

A)

Ho: p = 0.73

Ha: p 0.73

Test statistics

z = ( - ) / *(1-) / n

= ( 0.76 - 0.73) / (0.73*0.27) /1200

= 2.34

P-value = P(Z>z)

= 1 - P(Z <z )

= 1- P(Z < 2.34)

= 1 - 0.9904

= 0.0096

The p-value is p = 0.0096, and since p = 0.0096 < 0.10, it is concluded that the null hypothesis is rejected.