Question

A survey​ asks, "If the husband in a family wants​ children, but the wife decides that she does not want any​ children, is it all right for the wife to refuse to have​ children?" Of 723 ​subjects, 585 said yes. a. Find a​ 99% confidence interval for the population proportion who would say yes. ​( nothing​, nothing​) ​(Round to four decimal places as​ needed.)

Answer 1

Solution :

Given that,

n = 723

x = 585

Point estimate = sample proportion = = x / n =585/723=0.809

1 - =1 -0.809=0.191

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 (((0.809*0.191) /723 )

= 0.0377

A 99% confidence interval for p is ,

- E < p < + E

0.809-0.0377 < p < 0.809+0.0377

0.7713< p < 0.8467