Mathematics: 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 75% 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 72%. Determine the P-value of the test statistic. Round your answer to four decimal places.

The mayor of a town has proposed a plan for the annexation

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24.01.2022

P-value of the test statistic: P=0.0266.

Step-by-step explanation:

Hypothesis test on a proportion.

The claim is that the percentage of residents who favor annexation is above 72% This is going to be stated in the alternative hypothesis.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.72\\\\H_a:\pi0.72$

The sample size is n=900 and the sample proportion is p=0.75.

The standard devaition is calculated as:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.72*0.28}{900}}=\sqrt{0.000224}=0.015$

Then, the z-statistic is:

$z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.75-0.72-0.5/900}{0.015}=\dfrac{0.029}{0.015} = 1.9333$

For this right tailed test, the P-value is:

P-value=P(z0.1933)=0.0266

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