Question

Assume that a sample is used to estimate a population proportion p. Find the 99.5% confidence interval for a sample of size 175 with 75 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 = 75 / 175 = 0.429

1 - = 0.571

Z/2 = 2.576

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

= 2.576 * [(0.429 * 0.571) / 175]

= 0.096

A 99.5% confidence interval for population proportion p is ,

- E < p < + E

2.576 - 0.096 < p < 2.576 + 0.096

2.480 < p < 2.672

99.5% C.I. = (2.480, 2.672)