Question

In a random sample of 200 couples, the wife was taller than the husband in only 10 couples.

Construct a 99% confidence interval for the proportion of couples where the wife is taller

Answer 1

Solution :

Given that,

n = 200

x = 10

Point estimate = sample proportion = = x / n = 10/200=0.05

1 -   = 1- 0.05 =0.95

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

= 2.576* (((0.05*0.95) / 200)

E = 0.040

A 99% confidence interval for proportion p is ,

- E < p < + E

0.05-0.040 < p < 0.05+0.040

0.01 <p< 0.09

(0.01 , 0.09)