Question

Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value tα/2​, ​(b) find the critical value zα/2​, or​ (c) state that neither the normal distribution nor the t distribution applies.
The confidence level is 99​%, σ is not​ known, and the histogram of 56 player salaries​ (in thousands of​ dollars) of football players on a team is as shown.

Answer 1

Considering that we have the standard deviation for the sample, the t-distribution will be used, and the critical value is t = 2.6682.

When should the t-distribution and the z-distribution be used?

• If we have the standard deviation for the sample, the t-distribution should be used.

• If we have the standard deviation for the population, the z-distribution should be used.

In this problem, σ is not​ known, hence we get the standard deviation of the sample from the histogram and the t-distribution is used.

Using a t-distribution calculator, considering a confidence level of 99​% and 56 - 1 = 55 df, the critical value is t = 2.6682.

More can be learned about the t-distribution at brainly.com/question/16162795