Question

1.)If n=400 and X=100​, construct a 95​% confidence interval estimate of the population proportion. ≤π≤ (ROUND 4 DECIMAL PLACES)

2.) 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 120 of the households would purchase the additional telephone line at a reduced installation cost. a. Construct a 99​% confidence interval estimate for the population proportion of households that would purchase the additional telephone line. ≤π≤ (ROUND 4 DECIMAL PLACES)

Answer 1

1)

Sample proportion = 100 / 400 = 0.25

95% confidence interval for is

- Z * sqrt( ( 1 - ) / n) < < + Z * sqrt( ( 1 - ) / n)

0.25 - 1.96 * sqrt( 0.25 * 0.75 / 400) < < 0.25 + 1.96 * sqrt( 0.25 * 0.75 / 400)

0.2076 < < 0.2924

2)

Sample proportion = 120 / 500 = 0.24

99% confidence interval for is

- Z * sqrt( ( 1 - ) / n) < < + Z * sqrt( ( 1 - ) / n)

0.24 - 2.5758 * sqrt( 0.24 * 0.76 / 500) < < 0.24 + 2.5758 * sqrt( 0.24 * 0.76 / 500)

0.1908 < < 0.2892