Question

Two samples are taken with the following numbers of successes and sample sizes
r1r1 = 25 r2r2 = 24
n1n1 = 71 n2n2 = 67

Find a 98% confidence interval, round answers to the nearest thousandth.
____< p1−p2p1-p2 <____

Answer 1

Let be the two population proportions.

Also, let represent the sample proportions calculated as the ratio of the number of successes to the number of trials.

Based on the information given in the question,

And

A % confidence interval for the difference of proportions, , is given by:

where, and is the sample sizes,

is the critical value of the -distribution.

Here,

The left tail value of the normal distribution is computed using the command "=NORMSINV" in MS-EXCEL. The screenshot is shown below:

Therefore,

Since the normal distribution is symmetric, therefore, .

Therefore, the 98% confidence interval is:

  

Therefore the required 98% confidence interval is .