Question

An experimenter has prepared a drug-dose level that he claims will reduce headaches for 80% of people suffering from migraines. There is speculation that the claims regarding the effectiveness of his dosage are inflated (i.e., are too high). In attempt to prove this, we administer his prescribed dosage to 50 people with migraines and observe that 37 of them have had reduced headaches by the drug dose. Is there enough evidence to conclude that his claim is inflated at the 5% level of significance?

(A) Yes, because the p-value is equal to .1446, which is greater than .05.   (B) Yes, because 74% is less than 80% and the difference is more than 5%.   (C) No, because the p-value is equal to .1446, which is greater than .05.   (D) No, because −1.06 is not less than −1.96.   (E) Yes, because −1.06 is greater than −1.96.

Answer 1

The null and alternate hypothesis are:

The test statistic value is given by:

Since this is a left tailed test, so the p-value is given by:

Since p-value is greater than 0.01, so we do not have sufficient evidence to reject the null hypothesis H0.

So, we do not have sufficient evidence to conclude that the claim is inflated.

Hence option C is the correct option.