91影视

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:

$\begin{array}{l}(P_1鈭�P_2)卤z_{\frac{a}{2}}脳{蟽}_{(p1鈭�p2)}\\ (P_1鈭�P_2)卤z_{\frac{a}{2}}脳\sqrt{\frac{p_1{q}_1}{n_1}+\frac{p_2{q}_2}{n_2}}\end{array}$

Substituting the sample quantities yields

$(0.1843鈥�0.1769)卤1.96\sqrt{\frac{\left(0.1843\right)\left(0.8157\right)}{1145}+\frac{\left(0.1769\right)\left(0.8231\right)}{1142}}$

=- 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 ($P_1-P_2$).