Question

"Currently, only 20 percent of arrested drug pushers are convicted", cried candidate AK in a campaign speech. "Elect me and you'll see a big increase in convictions" A year after his election a random sample of 144 case files of arrested drug pushers showed 36 convictions. For a right-tailed test, find the p-value. A. 0.12 B. 0.07 C. 0.06 D. 0.04

Answer 1

B. 0.07

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:

`H_0: \pi=0.2\\\\H_a:\pi>0.2`

The sample has a size n=144.

The sample proportion is p=0.25.

`p=X/n=36/144=0.25`

The standard error of the proportion is:

`\sigma_p=\sqrt{(\pi(1-\pi))/(n)}=\sqrt{(0.2*0.8)/(144)}\\\\\\ \sigma_p=√(0.001111)=0.0333`

Then, we can calculate the z-statistic as:

`z=\frac{p-\pi}=(0.25-0.2)/(0.0333)=(0.05)/(0.0333)=1.5`

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

`\text{P-value}=P(z>1.5)=0.066\approx0.07`