Problem

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 95%,σ is not known, and the histogram of 55 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. tα/2=
(Round to two decimal places as needed.)
B. zα/2=
(Round to two decimal places as needed.)

Answer

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Answer

Final Answer: 2.00

Steps

Step 1 :Since the population standard deviation σ is not known and the sample size is less than 30, we should use the t-distribution to construct the confidence interval. Therefore, we need to find the critical value tα/2 for a 95% confidence level.

Step 2 :The degrees of freedom for a t-distribution is given by the sample size minus 1. In this case, the degrees of freedom is 551=54.

Step 3 :The value of α is 10.95=0.05. Since we are constructing a two-tailed test, we need to divide α by 2, which gives us 0.025.

Step 4 :Using these values, we can find the critical value tα/2.

Step 5 :The critical value tα/2 for a 95% confidence level with 54 degrees of freedom is approximately 2.00.

Step 6 :Final Answer: 2.00

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