Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value ta/2. (b) find the critical value z/2, or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 95%, o is not known, and the histogram of 62 player salaries (in thousands of dollars) of football players on a team is as shown.

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**Constructing a Confidence Interval**

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 95%, \( \sigma \) is not known, and the histogram of 62 player salaries (in thousands of dollars) of football players on a team is as shown.

**Graph Explanation:**
The histogram represents the distribution of 62 player salaries in thousands of dollars. The x-axis shows the salary in thousands, ranging from 0 to 20,000 dollars. The y-axis indicates the frequency of players within each salary range. The histogram shows a higher frequency of players in the lower salary ranges, with fewer players in the higher salary ranges.

**Graph Data:**
- Highest frequency is for the salary range near 0 to 2000 ($0 to $2000k).
- There is a decreasing frequency as the salary range increases.

**Question:**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

**Options:**
- \( \circ \) A. \( t_{\alpha / 2} = \_\_\_\_ \)  
*(Round to two decimal places as needed.)*

- \( \circ \) B. \( Z_{\alpha / 2} = \_\_\_\_ \)  
*(Round to two decimal places as needed.)*

- \( \circ \) C. Neither the normal distribution nor the t distribution applies.

*(Please select the correct option and fill in the necessary value if applicable.)*
Transcribed Image Text:**Constructing a Confidence Interval** 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 95%, \( \sigma \) is not known, and the histogram of 62 player salaries (in thousands of dollars) of football players on a team is as shown. **Graph Explanation:** The histogram represents the distribution of 62 player salaries in thousands of dollars. The x-axis shows the salary in thousands, ranging from 0 to 20,000 dollars. The y-axis indicates the frequency of players within each salary range. The histogram shows a higher frequency of players in the lower salary ranges, with fewer players in the higher salary ranges. **Graph Data:** - Highest frequency is for the salary range near 0 to 2000 ($0 to $2000k). - There is a decreasing frequency as the salary range increases. **Question:** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. **Options:** - \( \circ \) A. \( t_{\alpha / 2} = \_\_\_\_ \) *(Round to two decimal places as needed.)* - \( \circ \) B. \( Z_{\alpha / 2} = \_\_\_\_ \) *(Round to two decimal places as needed.)* - \( \circ \) C. Neither the normal distribution nor the t distribution applies. *(Please select the correct option and fill in the necessary value if applicable.)*
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