Question

Assume that a sample is used to estimate a population proportion p. Find the 99.5% confidence interval for a sample of size 163 with 135 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.

99.5% C.I. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 135 / 163 = 0.828

1 - = 1 - 0.828 = 0.172

Z/2 = 2.807

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

= 2.807 * (((0.828 * 0.172) / 163)

Margin of error = E = 0.083

A 95.5% confidence interval for population proportion p is ,

- E < p < + E

0.828 - 0.083 < p < 0.828 + 0.083

0.745 < p < 0.911

99.5% C.I. = 0.745 , 0.911