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 99​%, sigmaσequals=3210 thousand​ dollars, and the histogram of 62 player salaries​ (in thousands of​ dollars) of football players on a team is as shown.

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

t Subscript alpha divided by 2tα/2equals=

​(Round to two decimal places as​ needed.)

B.

z Subscript alpha divided by 2zα/2equals=

​(Round to two decimal places as​ needed.)

C.

Neither the normal distribution nor the t distribution applies.

Answer 1

Given that, population standard deviation = 3210 thousand dollars and sample size (n) = 62

confidence level = 0.99

=> significance level = 1 - 0.99 = 0.01 and

Since, population standard deviation is known, we should use standard normal z-critical value to find the confidence interval.

Using standard normal z-table we get, z-score corresponding probability of 0.005 is, z = -2.58

=> Critical values are -2.58, 2.58

Answer : b)