Calculating Critical Value for a 99% Confidence Level

What critical value is appropriate for a​ 99% confidence level where n​17; sigma is unknown and the population appears to be normally​ distributed?

A. z alpha/2 = 2.567

B. t alpha/2 = 2.921

C. z alpha/2 = 2.583

D. t alpha/2 = 2.898

Answer:

For a 99% confidence level with a sample size of 17 and unknown sigma, the appropriate critical value would be the t alpha/2 = 2.921. This is due to the smaller sample size and unknown population standard deviation, where usage of t-distribution is more appropriate.

For a 99% confidence level with a sample size of 17 (n=17), and sigma (population standard deviation) unknown, we would use a t-statistic. This is due to the fact that you have a small sample size and sigma is unknown, which makes the use of the normal distribution inappropriate. The population, although normally distributed, requires some approximation with n less than 30 and sigma unknown. This calls for a t-distribution.

A t alpha/2 value would be used in this case. The critical value would change depending on the confidence level of the interval. For the 99% confidence level for a two-tailed test, the t alpha/2 value corresponding to degrees of freedom df= n-1, which is equal to 16 (17-1 = 16), is usually referenced from a t-distribution table. Assuming that two tail values are used, the answer t alpha/2 = 2.921 should be appropriate.