Question

College students and STDs: A recent report estimated that 25% of all college students in the United States have a sexually transmitted disease (STD). Due to the demographics of the community, the director of the campus health center believes that the proportion of students who have a STD is lower at his college.

He tests H₀: p = 0.25 versus H_a: p < 0.25. The campus health center staff select a random sample of 50 students and determine that 18% have been diagnosed with a STD.

Is the sample size condition for conducting a hypothesis test for a population proportion satisfied?

A. Yes, because the sample is random. It represents the college students at this campus.

B. Yes, because (50)(.25) and (50)(1 ‑ 0.25) are both at least 10. This means we can use the normal distribution to model the distribution of sample proportions.

C. No, because (50)(0.18) is less than 10. Because of this the sample size is too small to use the normal distribution to model the distribution of sample proportions.

D. No, because 50 students is not enough to be representative of the students at the college

Answer 1

answer : B. Yes, because (50)(.25) and (50)(1 ‑ 0.25) are both at least 10. This means we can use the normal distribution to model the distribution of sample proportions.

Explanation :

The normal distribution is an appropriate model for this sampling distribution if the expected number of success and failures are both at least 10.

p: population proportion

n : sample size

np ≥ 10 and n(1 − p) ≥ 10.

Here p = 0.25 & n = 50

50(0.25) = 12.5 > 10

50(1-0.25) = 37.5 > 10

PL??