19A telecommunications company wants to estimate the proportion of households th

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 110 of the households would purchase the additional telephone line at a reduced installation cost ................ Construct a 95?% confidence interval estimate for the population proportion of households that would purchase the additional telephone line.

Explanation / Answer

p = 110/500 = 0.22

standard error = sqrt(p*(1-p)/n)

= sqrt(0.22*0.78/500)

= 0.01853

margin of error = 0.01853 * 1.96 = 0.0363

lower limit = 0.22 - 0.0363 = 0.1837

upper limit = 0.22 + 0.0363 = 0.2563

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