"Currently,only 20 percent of arrested drug pushers are convicted," cried candidate Courageous Calvin 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,the p-value is approximately
A).9332
B).0668
C).0435
D).0250

Question

Quizplus · Accepted Answer

The null hypothesis is that the conviction rate remains the same as before, i.e, p = 0.20.
The alternative hypothesis is that the conviction rate has increased after the election, i.e, p > 0.20.
Since this is a right-tailed test, we need to find the area to the right of the observed proportion of convictions (36/144 = 0.25).

Using the normal approximation to the binomial distribution, we get:
z = (p̂ - p) / √(p(1-p)/n)
where p̂ = 0.25 (observed proportion of convictions), p = 0.20, n = 144 (sample size)

Plugging in the values, we get:
z = (0.25 - 0.20) / √(0.20(1-0.20)/144) = 1.83

Looking up the area to the right of z = 1.83 in the standard normal distribution table, we get the p-value as 0.0336.
However, since this is a right-tailed test, we need to subtract this value from 1 to get the final p-value:
p-value = 1 - 0.0336 = 0.0664 (approximately)

Therefore, the best choice is B, with a p-value of 0.0668. There is not enough evidence to reject the null hypothesis at a significance level of 0.05 or lower, which means we cannot conclude that there has been a significant increase in convictions after the election.

"Currently,only 20 Percent of Arrested Drug Pushers Are Convicted," Cried