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 180 of the households would purchase the additional telephone line at a reduced installation cost. Complete parts (a) and (b) below. a. Construct a 95% confidence interval estimate for the population proportion of households that would purchase the additional telephone line. ? ? round to four decimal places as needed

Explanation / Answer

p is 180/500=0.36

z for 95% confidence is 1.96

lower bound is p-z*sqrt(p*(1-p)/N)=0.36-1.96*sqrt(0.36*(1-0.36)/500)=0.3179

upper bound is p+z*sqrt(p*(1-p)/N)=0.36+1.96*sqrt(0.36*(1-0.36)/500)=0.4021

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