Question

in a simple random sample of 100 allergy sufferers, 15 of them reported obtaining relief from a new allergy medication. is it appropriate to use the methods of this section to perform a hypothesis test about the proportion of allergy sufferers who experience relief from this medication? if not, why not?
○ no, the sample size is too large in comparison with the population.
○ no, the number of responses in each category is not greater than 10.
○ yes, it is appropriate.

Explanation:

To determine appropriateness for a proportion hypothesis test, we check the success - failure condition. The number of "successes" (relief) is \(n\hat{p}=15\) and "failures" (no relief) is \(n(1 - \hat{p})=100 - 15 = 85\). The rule is that both \(n\hat{p}\) and \(n(1 - \hat{p})\) should be at least 10. Here, 15 (successes) and 85 (failures) are both greater than 10, so the methods are appropriate.

Answer:

Yes, it is appropriate.