Question

19A telecommunications company wants to estimate the proportion of households that would purchase an additional telephone line if it were made available at a substantially reduced installation cost. Data are collected from a random sample of 500 households. The results indicate that 145 of the households would purchase the additional telephone line at a reduced installation cost. Complete parts​ (a) and​ (b) below. a. Construct a 99​% confidence interval estimate for the population proportion of households that would purchase the additional telephone line.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 145 / 500 = 0.290

1 - = 1 - 0.290 = 0.71

Z_/2 = 2.576

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

= 2.576 * (((0.290 * 0.71) / 500)

= 0.052

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.290 - 0.052 < p < 0.290 + 0.052

0.238 < p < 0.342

The 99% confidence interval for the population proportion p is : 0.238 , 0.342