Question

Researchers want to test to see if the recovery rate of the coronavirus is different between Mexico and Italy. They take random samples of 250 and 300 patients, from Mexico and Italy respectively. 78 of the patients from Mexico had recovered. 84 patients from Italy had recovered. Conduct a hypothesis test using a significance level of α = 0.05 to determine if there is evidence that the proportion of Mexican patients who have recovered is larger than the proportion of Italian patients who have recovered.

(a) Is it appropriate to use the normal approximation for the sampling distribution of the difference in proportions?

(b) State the null and alternative hypotheses.

(c) Calculate the test statistic; z ∗ = q pˆ1−pˆ2 pc(1−pc) n1 + pc(1−pc) n2 , where ˆpc = n1pˆ1+n2pˆ2 n1+n2 .

(d) Find the P-value using the test statistic from (b) and the standard normal table.

(e) State the conclusion of the hypothesis test and what it means in terms of the original problem.

Answer 1