Question

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 Ha: 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.
a) Is the sample size condition for conducting a hypothesis test for a population proportion satisfied?

Answer 1

Explanation:

Given :

Answer 2

The sample size condition for conducting a hypothesis test for a population proportion is satisfied for this question.

Explanation:

a) The sample size condition for conducting a hypothesis test for a population proportion is satisfied is when

np > 5 and n(1 - p) > 5

n = sample size = 50

p = proportion that have STD = 18% = 0.18

np = 0.18 × 5 = 9 > 5

n(1 - p) = 0.82 × 50 = 41 > 5

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