Angioplasty’s benefits are challenged. Further, more than 1 million heart cases each time suffer an angioplasty. The benefits of an angioplasty were challenged in a study of cases (2007 Annual Conference of the American. College of Cardiology, New Orleans). All the cases had substantial blockage of the highways but were medically stable. All were treated with drugs similar to aspirin and beta-blockers. Still, half the cases were aimlessly assigned to get an angioplasty, and half were not. After five years, the experimenter planted 211 of the. Cases in the angioplasty group had posterior heart attacks compared with 202 cases in the drug-only group. Do you agree with the study’s conclusion? “There was no significant difference in the rate of heart attacks for the two groups”? Support your answer with a 95-confidence interval.

The two samples represent independent binomial trials. The arbitrary binomial variables are the figures x₁ and x₂ of the 1145 and 1142 cases in the angioplasty group and drug-only group, respectively.

The results are epitomized in the table over.

We now calculate the sample proportions P₁ and P₂ .Of the dropouts in the 1st and 2nd group Independently.

$\begin{array}{l}{P}_1=\frac{x_1}{n_1}=\frac{211}{1145}=0.1843\\ P_2=\frac{x_2}{n_2}=\frac{202}{1142}=0.1769\end{array}$

A large sample 95% confidence interval for the difference (P_{1 - P2}) between the drop rates of the two groups of exercisers is given by:

$\begin{array}{l}(P_1-P_2)\pm z_{\frac{a}{2}}\times {\sigma }_{(p1-p2)}\\ (P_1-P_2)\pm z_{\frac{a}{2}}\times \sqrt{\frac{p_1{q}_1}{n_1}+\frac{p_2{q}_2}{n_2}}\end{array}$

Substituting the sample quantities yields

$(0.1843–0.1769)\pm 1.96\sqrt{\frac{\left(0.1843\right)\left(0.8157\right)}{1145}+\frac{\left(0.1769\right)\left(0.8231\right)}{1142}}$

=- 0.00740.03153

= (- 0.02413, - 0.03893)

The interval can be interpreted as follows:

With a confidence coefficient equal to 0.95, we estimate that the difference in the rate of the heart attacks between the cases in the angioplasty group and the cases in the medication-only group falls in the interval from -0.02431 to 0.03893.

In other words, we estimate (with 95% confidence) the rate of heart attack for the medication-only group to be anywhere from 2.413% less than to 3.893% more than the heart attack rate for the angioplasty group.

There is insufficient evidence to indicate that ($P_1-P_2$)differs from 0 because the interval includes 0 as a possible value for ($P_1-P_2$).