Question 1182683: 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 normal quantile plot of the 17 salaries (in thousands of dollars) of basketball players on a team is as shown.
Select the correct choice below and, if necessary, fill in the blank to complete your choice.
A. tα/2 = __
(Round to two decimal places as needed.)
B. zα/2 = __
(Round to two decimal places as needed.)
C. Neither the normal distribution nor the t distribution applies.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! The correct choice is **A. tα/2 = __**
Here's why:
1. **σ is not known:** When the population standard deviation (σ) is unknown, we use the t-distribution to construct confidence intervals.
2. **Normal quantile plot:** The normal quantile plot helps us assess if the sample data comes from a normally distributed population. If the data is approximately normal, then the t-distribution is appropriate. A roughly linear pattern on the normal quantile plot suggests that the data are approximately normally distributed. Since we have a normal quantile plot, we can assume that the underlying population is normally distributed.
3. **Calculating tα/2:**
* Confidence level = 95% = 0.95
* α = 1 - Confidence level = 1 - 0.95 = 0.05
* α/2 = 0.05 / 2 = 0.025
* Degrees of freedom (df) = n - 1 = 17 - 1 = 16
Now, look up the t-value corresponding to α/2 = 0.025 and df = 16 in a t-table or use a calculator. You should find a value of approximately 2.12.
Therefore, tα/2 = **2.12**
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