Matched or Paired Samples · Exercise 17

A new heart disease prevention drug was tried on a group of 224 patients. Forty-five patients developed heart disease after four years. In a control group of 224 patients, 68 developed heart disease after four years. We want to test whether the method of treatment reduces the proportion of patients that develop heart disease after four years or if the proportions of the treated group and the untreated group stay the same.

Let the subscript t = treated patient and ut = untreated patient.

The appropriate hypotheses are:

(a) H_0: p_t < p_ut and H_a: p_t ≥ p_ut
(b) H_0: p_t ≤ p_ut and H_a: p_t > p_ut
(c) H_0: p_t = p_ut and H_a: p_t ≠ p_ut
(d) H_0: p_t = p_ut and H_a: p_t < p_ut

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §10.4 Matched or Paired Samples · Exercise 17