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 94.8%.
(Report answer accurate to three decimal places with appropriate rounding.)
za/2 =
In order to find the critical value that corresponds to a confidence level of 94.8%, we need to first determine the alpha level (α) associated with this confidence level.
The alpha level is equal to 1 minus the confidence level. So,
α = 1 - 0.948 = 0.052
Since we have a two-tailed test, we need to split the alpha level equally between the two tails of the distribution. So,
α/2 = 0.052/2 = 0.026
Now, we can find the critical value corresponding to the alpha/2 level in the standard normal distribution. We can use a standard normal table or use a calculator to find the z-value associated with an area of 0.026 in the tail.
Using a calculator or a standard normal table, we find that the critical value (denoted as za/2) that corresponds to an area of 0.026 in the tail is approximately -1.964.
Therefore, the critical value that corresponds to a confidence level of 94.8% is -1.964 (rounded to three decimal places).