Respuesta :
Answer:
B. 0.07
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion of convicted drug pushers is significnalty higher than 20%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.2\\\\H_a:\pi>0.2[/tex]
The sample has a size n=144.
The sample proportion is p=0.25.
[tex]p=X/n=36/144=0.25[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.2*0.8}{144}}\\\\\\ \sigma_p=\sqrt{0.001111}=0.0333[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi}=\dfrac{0.25-0.2}{0.0333}=\dfrac{0.05}{0.0333}=1.5[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>1.5)=0.066\approx0.07[/tex]
