Question

In a random sample of 200 British couples, the wife is taller than the husband in 10 of the couples. What is the upper bound for a 95% confidence interval for the proportion of all married British couples where the wife is taller than the husband? Round to at least 3 decimal places.

Answer 1

Solution :

Given that,

n = 200

x = 10

= x / n = 10/200 = 0.05

1 - = 1 - 0.05= 0.95

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.05 * 0.95) / 200) = 0.030

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.05 - 0.030 < p < 0.05 + 0.030

0.020 < p < 0.080

The 95% confidence interval for the population proportion p is : (0.020 ,  0.080)