Question

treating circulatory disease: angioplasty is a medical procedure in which an obstructed blood vessel is widened. in some cases, a wire mesh tube, called a stent, is placed in the vessel to help it remain open. a study was conducted to compare the effectiveness of a bare metal stent with one that has been coated with a drug designed to prevent reblocking of the vessel. a total of 5326 patients received bare metal stents, and of these, 842 needed treatment for reblocking within a year. a total of 1123 received drug - coated stents, and 148 of them required treatment within a year. can you conclude that the proportion of patients who needed retreatment differs between those who received bare metal stents and those who received drug - coated stents? let $p_1$ denote the proportion of patients with bare metal stents who needed retreatment and $p_2$ denote the proportion of patients with drug - coated stents who needed retreatment. use the $\alpha = 0.05$ level of significance and the $p$-value method with the ti - 84 plus calculator.
part: 0 / 4
part 1 of 4
state the appropriate null and alternate hypotheses.
$h_0:$ $\square$
$h_1:$ $\square$
this hypothesis test is a select test.

Explanation:

Step1: Define Hypotheses

We want to test if the proportion of patients needing retreatment differs between bare metal stents ($p_1$) and drug - coated stents ($p_2$). The null hypothesis assumes no difference, and the alternative hypothesis assumes a difference.
So, $H_0:p_1 = p_2$ and $H_1:p_1
eq p_2$. This is a two - tailed test because we are looking for a difference (either $p_1>p_2$ or $p_1 < p_2$), not a one - sided difference.

Answer:

$H_0:p_1 = p_2$; $H_1:p_1
eq p_2$; This hypothesis test is a two - tailed test.