Question

let p1 and p2 be the respextive proprtions of women with nutriomal anemia in each of two developing countries. if a random sample of 250 women from the first country yieled 90 women with the nutritional anemia and an indepently chosen random sample of 325 women delm the second countey yieled 100 women with the nutritional anemia find a 90% confidence interval for P1-P2.

what is the lower limit and upper limit of the 90% confidence interval.

Answer 1

= 90/250 = 0.36

= 100/325 = 0.308

The pooled sample of (P) = ( * n1 + * n2)/(n1 + n2)

= (0.36 * 250 + 0.308 * 325)/(250 + 325)

= 0.3306

At 90% confidence interval the critical value is z_0.05 = 1.645

The 90% confidence interval for (P1 - P2) is

() +/- z_0.05 * sqrt(P(1 - P)(1/n1 + 1/n2))

= (0.36 - 0.308) +/- 1.645 * sqrt(0.3306 * (1 - 0.3306) * (1/250 + 1/325))

= 0.052 +/- 0.0651

= -0.0131, 0.1171

Lower limit = -0.0131

Upper limit = 0.1171