MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:### Constructing a Confidence Interval
Assume that we want to construct a confidence interval. Do one of the following, as appropriate:
1. Find the critical value \( t_{\alpha / 2} \)
2. Find the critical value \( z_{\alpha / 2} \)
3. State that neither the normal distribution nor the t distribution applies.
### Problem Details:
- The confidence level is 90%
- The standard deviation \( \sigma \) is not known
- We have a histogram of 60 player salaries (in thousands of dollars) of football players on a team as shown below:
#### Histogram Description:
- The x-axis represents the salary in thousands of dollars, ranging from 0 to 20,000.
- The y-axis represents the frequency of players with those salaries.
- The histogram is skewed to the right, with most of the players having salaries between 0 to 4000 thousand dollars.
- The frequency of players with salaries in the 0-4000 range is the highest, exceeding 30 players.
- Some players have salaries between 4000-8000, with the frequency decreasing significantly.
- A few outliers have salaries between 8000-20000.
### Instructions:
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
**Options:**
- **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.
Use the dropdown options provided to make your selection and input your answers where required.
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