Effects of an appetite suppressant. Subject with preexisting cardiovascular symp

Step 1
(a) In the survey, out of 4,906 subjects in the sibutramine group of 561 subjects experienced the primary outcome and out of 4,898 subjects in the placebo group of 490 subjects experienced the primary outcome.
The proportion of subjects experiencing the primary outcome for the sibutramine group is,
${\displaystyle P_{sibutramine}=\frac{561}{4,906}}$
${\displaystyle =0.114}$
Thus, the proportion of subjects experiencing the primary outcome for the sibutramine group is 0.114.
The proportion of subjects experiencing the primary outcome for the placebo group is,
${\displaystyle P_{placebo}=\frac{490}{4,898}}$
${\displaystyle =0.100}$
Thus, the proportion of subjects experiencing the primary outcome for the placebo group is 0.100.
Step 2
(b) The general conditions to use the large-sample confidence interval are given below:
Two samples are simple random sample from two distinct populations.
The samples are independent.
Both populations are normally distributed.
The counts of successes and failures are five or more in both the samples.
In the survey, the two samples are randomly selected and independent. Moreover, the counts of successes and failures are larger. Hence, the large-sample confidence interval for comparing the proportions of sibutramine and placebo subjects who experienced the primary outcome can be used safely.
Let p1 denote the proportions of sibutramine subjects who experienced and primary outcome and p2 denote the proportions of placebo subjects who experienced the primary outcome. Here, compute the ${\displaystyle 95\mathrm{\%}}$ confidence interval for the difference between the proportions of sibutramine and placebo subjects who experienced primary outcome by using TI-83 graphing calculator.
Confidence interval using TI-83 graphing calculator:
Press STAT>TESTS>2-PropZInt.
Enter x1 as 561, n1 as 4,906, x2 as 490, n2 as 4,898.
C-level: as “0.95”.
Select Calculate and press “Enter”.
Output:
2-PropZInt
(.00207, .02655)
${\displaystyle p_1=.1143497758}$
${\displaystyle p_2=.100040833}$
${\displaystyle n_1=4906}$
${\displaystyle n_2=4898}$
From the output, the ${\displaystyle 95\mathrm{\%}}$ confidence interval for the difference between the proportions of sibutramine and placebo subjects who experienced the primary outcome is (0.0021,0.0266).
CONCLUDE:
There is ${\displaystyle 95\mathrm{\%}}$ confident that the difference between the proportions of sibutramine and placebo subjects who experienced the primary outcome lies between ${\displaystyle 0.21\mathrm{\%}}$ and ${\displaystyle 2.66\mathrm{\%}}$.