Question

Assume that a sample is used to estimate a population proportion p. Find the 95% confidence interval for a sample of size 252 with 79% successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.

< p <

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.79

1 - = 1 - 0.79 = 0.21

Z/2 = 1.96

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

= 1.96 * (((0.79 * 0.21) / 252)

Margin of error = E = 0.050

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.79 - 0.050 < p < 0.79 + 0.050

0.740 < p < 0.840