You intend to estimate a population proportion with a confidence interval.

Question

You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a reasonable approximation for the binomial distribution in this case.

While it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 86.4%.

(Report answer accurate to three decimal places with appropriate rounding.)

Answer 1

For confidence level 86.4% the level of significance (alpha) is (100 - 86.4)/100 = 0.136.

The critical value from the standard normal probability table is the z-score that corresponds to 1 - alpha/2 = 1 - 0.068 = 0.932.

Using the table, the critical z-score is approximately 1.49.