You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 18.
While it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 91.2%.
(Report answer accurate to three decimal places with appropriate rounding.)
ta/2 =
To find the critical value that corresponds to a confidence level of 91.2%, we need to find the z-score that corresponds to the tail probability of 0.095.
Since the given confidence level is uncommon, we need to divide (1 - 0.912) by 2 to get the tail probability in each tail: (1 - 0.912) / 2 = 0.044.
Now, we can use a standard normal distribution table or a calculator to find the z-score that corresponds to a tail probability of 0.044. Looking up this tail probability, we find that the corresponding z-score is approximately 1.699.
Therefore, the critical value that corresponds to a confidence level of 91.2% is approximately 1.699.