Question

Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate:...

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 2​, ​(b) find the critical value z Subscript alpha divided by 2​, or​ (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 90​%, sigma is not​ known, and the histogram of 58 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/alpha/2?

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

B.

z/ alpha/2?

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

C.

Neither the normal distribution nor the t distribution applies.

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Answer #1

Solution:

The confidence level is 90​%, sigma is not​ known, then we use t-distribution.

A)

sample size = n = 58

Degrees of freedom = df = n - 1 = 57

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t /2,df = t0.05,57 = 1.67

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