Question

Assume that a sample is used to estimate a population proportion p. Find the 80% confidence interval for a sample of size 102 with 79 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.

C.I. =

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 78 / 102 = 0.775

1 - = 1 - 0.775 = 0.225

Z/2 = 1.282

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

= 1.282 * (((0.775 * 0.225) / 102)

Margin of error = E = 0.053

A 80% confidence interval for population proportion p is ,

- E < p < + E

0.775 - 0.053 < p < 0.775 + 0.053

0.722 < p < 0.828

C.I. = 0.722 , 0.828