Statistic Word Problem

Question

Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value t Subscript alpha divided by 2tα/2, (b) find the critical value z Subscript alpha divided by 2zα/2, or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 9999%, sigmaσ is not known, and the histogram of 5555 player salaries (in thousands of dollars) of football players on a team is as shown.

Answer 1

You can can use or consult a T-Distribution table (when population standard deviation is unknown) and the Normal or Z-Distribution table to get critical values or you can use both "T-Interval" and "Z-Interval" programs contained in TI-83 and higher graphing calculators to compute the values as well.

Since you are dividing alpha value by two, this implies you are looking for a two-tail confidence interval or hypothesis testing critical values.

Thus the critical values for Part B is ±3.891

Part A, assuming your sample size as indicated in your problem is 5,555, your critical values at an alpha of .01 two tails approximates ±2.576

Part C, you apply t-distribution and values because population standard deviation is unknown