ndenice level is 9970, thou na dollarS, and the histogra m of 64 player salaries (in thousands llars) of TOotball players ona team is as showm. ect the correct choice below and, if necessary, fl in the answer box to complete your choice. A. 4/2= (Round to two decimal places as needed.) в. Za/2 =| (Round to two decimal places as needed.) c. Neither the normal distribution nor the t distribution applies.

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Chapter1: Starting With Matlab
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Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value \( t_{\alpha/2} \), (b) find the critical value \( z_{\alpha/2} \), or (c) state that neither the normal distribution nor the t distribution applies.

The confidence level is 99%, \( \sigma = 4108 \) thousand dollars, and the histogram of 64 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. \( t_{\alpha/2} = \square \)

   (Round to two decimal places as needed.)

B. \( z_{\alpha/2} = \square \)

   (Round to two decimal places as needed.)

C. Neither the normal distribution nor the t distribution applies.

---

**Histogram Explanation:**

- 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 specific salary ranges.
- The histogram shows a high frequency at lower salary ranges, with the highest bar around 0 to 4,000 thousand dollars, gradually decreasing towards salaries over 8,000 thousand dollars.
- There are few, if any, players with salaries above 12,000 thousand dollars.
- The distribution appears to be right-skewed, indicating that most players earn less while a few earn significantly more.
Transcribed Image Text:Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value \( t_{\alpha/2} \), (b) find the critical value \( z_{\alpha/2} \), or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 99%, \( \sigma = 4108 \) thousand dollars, and the histogram of 64 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. \( t_{\alpha/2} = \square \) (Round to two decimal places as needed.) B. \( z_{\alpha/2} = \square \) (Round to two decimal places as needed.) C. Neither the normal distribution nor the t distribution applies. --- **Histogram Explanation:** - 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 specific salary ranges. - The histogram shows a high frequency at lower salary ranges, with the highest bar around 0 to 4,000 thousand dollars, gradually decreasing towards salaries over 8,000 thousand dollars. - There are few, if any, players with salaries above 12,000 thousand dollars. - The distribution appears to be right-skewed, indicating that most players earn less while a few earn significantly more.
Expert Solution
Step 1

As the population standard deviation is known, we will use z test.

Histogram shows that the distribution of the population is skewed, but we will assume the normal because sample size is higher than 30 (from the standard normal table).

To find the critical value for a two-tailed test, use the standard normal table to find the z-score, which cuts off an area of 0.005 in the right tail of the normal curve and 0.005 in the left of the normal curve. Hence, the critical value of z at the 99% confieence level, i.e., 10% level of significance is 2.58   

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