A new drug is being proposed for the treatment of migraine headaches. Unfortunately, some users in early tests of the drug have reported mild nausea as a side effect. The FDA will reject the drug if it thinks that more than 15% (i.e. 0.15) of the population would suffer from this side effect. In an experiment to test this side effect, 400 people who suffer from migraine headaches receive the new drug and 80 of them report nausea as a side effect.
1. Carry out a hypothesis test to determine if the FDA should reject the drug. Use 5% significance level.

We are given that a new drug is being proposed for the treatment of migraine headaches. The FDA will reject the drug if it thinks that more than 15% (i.e. 0.15) of the population would suffer from this side effect.

Let, NULL HYPOTHESIS, [tex]H_0[/tex] : p [tex]\leq[/tex] 15% {means that the % of population that suffer from this side effect is less than or equal to 15%}

ALTERNATE HYPOTHESIS, [tex]H_1[/tex] : p > 15% {means that the % of population that suffer from this side effect is more than 15%}

Also, in an experiment to test this side effect, 400 people who suffer from migraine headaches receive the new drug and 80 of them report nausea as a side effect.

The test statistics that will be used here is One-sample z proportion test;

T.S. = [tex]\frac{\hat p - p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)

where, [tex]\hat p[/tex] = proportion of people who suffer from migraine headaches in an

experiment of 400 people = [tex]\frac{80}{400}[/tex] = 0.20

n = sample of people = 400

So, test statistics = [tex]\frac{0.20 - 0.15}{\sqrt{\frac{0.20(1-0.20)}{400} } }[/tex]

= 2.50

Now, at 5% significance level z table gives critical value of 1.6449. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.

Therefore, we conclude that % of population that suffer from this side effect is more than 15% which means FDA should reject the drug.