A mammologist collected 90 female kangaroo rats and 27 of th

A mammologist collected 90 female kangaroo rats and 27 of them were pregnant. Use the normal distribution to find a 95% confidence interval for the pregnancy rate in female kangaroo rats. show work

Solution

p=27/90 = 0.3

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So 95% confidence interval for the pregnancy rate in female kangaroo rats is

p +/- Z*sqrt(p*(1-p)/n)

--> 0.3 +/- 1.96*sqrt(0.3*0.7/90)

--> (0.205323, 0.394677)