Sample sizes question

Question

Two samples are taken with the following numbers of successes and sample sizes

r1 = 20  r2 = 30

n1 = 50  n2 = 52

Find a 85% confidence interval, round answers to the nearest thousandth.

Incorrect< p1−p2<

Answer 1

Hi Monem,

I don't know what technology you can use to solve this problem.

The simplest way is using the site www.wolframalpha.com

Enter in Search field: two proportion interval

In Computational Inputs enter corresponding values.

85% confidence interval: -0.3172 < p1-p2 < -0.03666

If you have to calculate confidence interval by formula, use the formula

(r₁/n₁ - r₂/n₂) ± z_c √(r₁(n₁ - r₁)/n₁³ + r₂(n₂ - r₂)/n^₂3)

where z_c is the critical value corresponding 85% confidence.

You can find this value either with table of normal distribution (details depend on a form of such table), or using calculator like TI-36, TI-83, or TI-84, or again on site www.wolframalpha.com if you enter in Search field: normal probability.

For 85% confidence z_c = 1.44.