Question

The mayor of a town has proposed a plan for the construction of an adjoining community. A political study took a sample of 12001200 voters in the town and found that 26%26% 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 not equal to 29%29%. Testing at the 0.050.05 level, is there enough evidence to support the strategist's claim?

Step 1 of 7:

State the null and alternative hypotheses.

Answer 1

n=1200, = 26%= 0.26

1)

Ho: P= 0.29

Ha: P 0.29

2)

it is two tailed z propotion test.

level of significance = 0.05

3)

formula for test statistics is

test statistics= -2.29

4)

now calculate critical values for two tailed test with 0.05 significance level.

critical values are = ( -1.96 , 1.96 )

5)

calculate P-value

P-Value = 2 * p(z< -2.29)

using normal z table we get

p(z< -2.29)= 0.0110

p-value = 2* 0.0110

P-Value= 0.0220

6)

since ( P-Value= 0.0220) < ( =0.05 )

hence, Null hypothesis is rejected.

7)

Therefore there is enough significant evidence to support the claim that the percentage of residents who favor construction is not equal to 29%