Question

Assume that a sample is used to estimate a population proportion p. Find the 99.5% confidence interval for a sample of size 165 with 91 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 1

The solution step-by-step.

To calculate the confidence interval, we must find p′, q′.

n = 165

x = the number of successes in the sample = 91

is the sample proportion; this is the point estimate of the population proportion.

Since the requested confidence level is CL = 0.995, then

This may be found in the students t table at the 0.025 column and infinity degrees of freedom because at infinite degrees of freedom the students t distribution becomes the standard normal distribution, Z.

The confidence interval for the true binomial population proportion is

Substituting in the values from above we get we find the Confidence Interval is

rounded off to three decimal places