Question

The mayor of a town has proposed a plan for the construction of an adjoining community. A political study took a sample of 900 voters in the town and found that 45% 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 over 42%. Determine the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

Answer:

P-value = 0.0367

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the percentage of residents who favor construction is significantly over 42%.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.42\\\\H_a:\pi>0.42$

The sample has a size n=900.

The sample proportion is p=0.45.

 

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.42*0.58}{900}}\\\\\\ \sigma_p=\sqrt{0.000271}=0.016$

Then, we can calculate the z-statistic as:

$z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.45-0.42-0.5/900}{0.016}=\dfrac{0.029}{0.016}=1.79$

This test is a right-tailed test, so the P-value for this test is calculated as:

$\text{P-value}=P(z>1.79)=0.0367$