Question

A medical study wanted to test the claim that stent implantation was less effective for clearing arteries of plaque than medical therapy alone. 15.6% of the patients treated with medical therapy alone experienced another cardiovascular event (heart attack, stroke or death) within four years of their surgery. 187 of the 1,083 patients treated with stent implantation experienced another cardiovascular event (heart attack, stroke or death) within four years of their surgery. Test the medical study's claim at a 0.01 level of significance that more patients suffered a heart attack, a stroke or died after their surgery.

Answer 1

Let p be the true proportion of patients treated with stent implantation experienced another cardiovascular event within four years of their surgery

Null Hypothesis H0: p = 0.156

Alternative Hypothesis H0: p > 0.156

np(1-p) = 1083 * 0.156 * (1 - 0.156) = 142.5921

Since, np(1-p) > 10, the sample size is large enough to assume that the sampling distribution of proportion is normal and we can use one sample z test.

Significance level = 0.01

Decision - Reject null hypothesis H0 if p-value is less then 0.01

Standard error of mean, SE = = 0.01102603

Sample proportion,  = 187/1083 = 0.1726685

Test statistic, z = ( - p) / SE = (0.1726685 - 0.156) / 0.01102603 = 1.51

P-value = P(z > 1.51) = 0.0655

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence from the sample data that true proportion of patients treated with stent implantation experienced another cardiovascular event within four years of their surgery is greater than 0.156. Hence we cannot significantly conclude that the stent implantation was less effective for clearing arteries of plaque than medical therapy alone.