Question

The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900 voters in the town and found that 61% 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 above 57%. Determine the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

The following information is provided: The sample size is N = 900, the number of favorable cases is X = 549 , and the sample proportion is $\bar p = \frac{X}{N} = \frac{ 549}{ 900} = 0.61$ , and the significance level is α=0.05

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: p = 0.57

Ha: p > 0.57

This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used.

(2) Test Statistics

The z-statistic is computed as follows:

$z = \frac{\bar p - p_0}{\sqrt{p_0(1-p_0)/n}}$

$z= \frac{ 0.61 - 0.57 }{\sqrt{ 0.57(1- 0.57)/900}} = 2.424$  

Using the P-value approach: The p-value is p = 0.0077