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 94%.
(Report answer accurate to three decimal places with appropriate rounding.)
To find the critical value that corresponds to a confidence level of 94%, we need to find the z-score associated with this confidence level.
A 94% confidence level means that the alpha (α) level is (1-0.94) = 0.06.
Since the normal distribution is symmetric, we need to find the z-score that corresponds to an alpha level of 0.03 (half of 0.06) in the standard normal distribution.
Using a standard normal distribution table or a calculator, we can find that the z-score that corresponds to an alpha level of 0.03 is approximately 1.880.
Therefore, the critical value that corresponds to a 94% confidence level is approximately 1.880.