Assume that a sample is used to estimate a population proportion p. Find the 99.5% confidence interval for a sample of size 87 with 37.9% successes.

Question

Assume that a sample is used to estimate a population proportion p. Find the 99.5% confidence interval for a sample of size 87 with 37.9% 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

p hat = 37.9% = 0.379

CI = p hat ± z sqrt (p hat (1-p hat)/n)

n = 87

For a 99.5 % CI, Z = 2.58

On a TI-84 you can find this using

invNorm, area = 0.995, mean =0, sd = 1

CI

0.379 ± 0.134 SO (0.245, 0.513)