I'm practicing for a probability midterm, and I was wondering if someone can tell me if my answers are right or not.
Arkansas recently passed a law sparking a debate about a new treatment. The treatment is supposed to help a person’s pregnancy continue under conditions that usually end it.
Usually, under those conditions, only about 40% of people’s pregnancies continue. But in a small case study, six pregnant people were given the new treatment, and four of them continued their pregnancies.
Critics say this result is not significant: it doesn’t show the treatment has an effect.
Use a normal approximation to assess this criticism. The null hypothesis is that each pregnancy is a “trial” with 0.4 probability of “success”.
(a) What are μ and σ in the case study?
In this case, the mean is 4 people. The standard deviation is $\sqrt(npq) = \sqrt(10*0.4*0.6) = 1.5$
(b) Are the results of the case study significant at the .05 level?
I believe this is a personal question, personally I'm assuming this means two standard deviations away or 3 people, which I'd say yes since 3 people out of 10 is a lot.
(c) Suppose a much larger study were done, with 150 subjects getting the treatment, and two/thirds of them continuing their pregnancies. What would μ and σ be then? Would the results be significant at the .01 level?
This makes μ $= 150 * 2/3 = 100$, and σ = $\sqrt(150*2/3*1/3) = 5.77$. In this case, .01 is is three standard deviations away, which means 17 people. Personally, that still seems worth it.
Do these answer make sense?