Question

The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 900 voters in the town and found that 75% 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 72%. Testing at the 0.05 level, is there enough evidence to support the strategist's claim?

Answer 1

Solution :

Given that,

= 0.72

1 - = 0.28

n = 900

Level of significance = = 0.05

Point estimate = sample proportion = = 0.75

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.72

Ha: p 0.72

Test statistics

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

= ( 0.75 - 0.72) / (0.72*0.28) / 900

= 2.004

P-value = P(Z>z)

= 1 - P(Z <z )

= 1- P(Z < 2.004)

= 0.0225

The p-value is p = 0.0225, and since p = 0.0225 < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the percentage of residents who favor construction is more than 72%. at the α = 0.05 significance level.