Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tx/2. (b) find the critical value Za/2, or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 90%, 4030 thousand dollars, and the histogram of 66 player salaries (in thousands of dollars) of football players on a team is as shown. 4000 8000 12000 16000 20000 Salary (thousands of dollars) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. ta/2= (Round to two decimal places as needed.) OB. Za/27 (Round to two decimal places as needed.) O C. Neither the normal distribution nor the t distribution applies. Frequency 40 30- 20 10- 0 Q

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### Confidence Interval Construction for Player Salaries

**Objective:**
We aim to construct a confidence interval for player salaries. Depending on the situation, you can either:
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.

**Given Data and Conditions:**
- Confidence level: 90%
- Standard deviation (σ): 4030 thousand dollars
- A histogram representing 66 player salaries (in thousands of dollars) is provided.

**Histogram Analysis:**

The histogram shows the distribution of 66 player salaries. The x-axis represents salaries (in thousands of dollars), ranging from 0 to 20,000 thousand dollars. The y-axis denotes frequency. The salary distribution appears to be right-skewed, with the majority of player salaries clustered between 0 and 4,000 thousand dollars and fewer players earning higher salaries. Below is a detailed representation:

- Salary Range and Frequency:
  - 0 to 4000: Approximately 40 players
  - 4000 to 8000: Approximately 15 players
  - 8000 to 12000: Approximately 5 players
  - 12000 to 16000: Approximately 2 players
  - 16000 to 20000: Approximately 2 players

**Question:**
Given the above information, select the correct choice and fill in the necessary value:

1. **t_{\alpha/2}** (Round to two decimal places as needed.)
2. **z_{\alpha/2}** (Round to two decimal places as needed.)
3. Neither the normal distribution nor the t distribution applies.

**Choices:**
- **A.** \( t_{\alpha/2} = \) ___
- **B.** \( z_{\alpha/2} = \) ___
- **C.** Neither the normal distribution nor the t distribution applies.
Transcribed Image Text:### Confidence Interval Construction for Player Salaries **Objective:** We aim to construct a confidence interval for player salaries. Depending on the situation, you can either: 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. **Given Data and Conditions:** - Confidence level: 90% - Standard deviation (σ): 4030 thousand dollars - A histogram representing 66 player salaries (in thousands of dollars) is provided. **Histogram Analysis:** The histogram shows the distribution of 66 player salaries. The x-axis represents salaries (in thousands of dollars), ranging from 0 to 20,000 thousand dollars. The y-axis denotes frequency. The salary distribution appears to be right-skewed, with the majority of player salaries clustered between 0 and 4,000 thousand dollars and fewer players earning higher salaries. Below is a detailed representation: - Salary Range and Frequency: - 0 to 4000: Approximately 40 players - 4000 to 8000: Approximately 15 players - 8000 to 12000: Approximately 5 players - 12000 to 16000: Approximately 2 players - 16000 to 20000: Approximately 2 players **Question:** Given the above information, select the correct choice and fill in the necessary value: 1. **t_{\alpha/2}** (Round to two decimal places as needed.) 2. **z_{\alpha/2}** (Round to two decimal places as needed.) 3. Neither the normal distribution nor the t distribution applies. **Choices:** - **A.** \( t_{\alpha/2} = \) ___ - **B.** \( z_{\alpha/2} = \) ___ - **C.** Neither the normal distribution nor the t distribution applies.
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