Researchers suspect that $17 \%$ of all high school students smoke at least one pack of cigarettes a day. At Wilson High School, a randomly selected sample of 300 students found that 49 students smoke at least one pack of cigarettes a day. At $\alpha = 0.05$, test the claim that less than $17 \%$ of all high school students smoke at least one pack of cigarettes a day. Use the $P$-value method.
A) There is not enough information to draw a conclusion.
B) No. There is not enough evidence to support the claim that the percentage of students who smoke at least one pack of cigarettes a day is less than 17%.
C) Yes. There is enough evidence to support the claim that the percentage of students who smoke at least one pack of cigarettes a day is less than 17%.

Question

Quizplus · Accepted Answer

The sample proportion is 49/300 = 0.1633. The standard deviation of the sample proportion is sqrt(0.17 * 0.83 / 300) = 0.026. The z-score is (0.1633 - 0.17) / 0.026 = -0.254. The P-value is P(Z < -0.254) = 0.398. Since the P-value is greater than 0.05, we fail to reject the null hypothesis. There is not enough evidence to support the claim that the percentage of students who smoke at least one pack of cigarettes a day is less than 17%.

Researchers Suspect That 17%17 \%17% Of All High School Students Smoke at Least One Pack

Researchers Suspect That $17 \%$ Of All High School Students Smoke at Least One Pack