Answer:
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:
[tex]H_0: \pi=0.72\\\\H_a:\pi>0.72[/tex]
The sample size is n=900 and the sample proportion is p=0.75.
The standard devaition is calculated as:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.72*0.28}{900}}=\sqrt{0.000224}=0.015[/tex]
Then, the z-statistic is:
[tex]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[/tex]
For this right tailed test, the P-value is:
[tex]P-value=P(z>0.1933)=0.0266[/tex]
