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 Za/2, or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 90%, o is not known, and the histogram of 65 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. OA. 1/2 B. (Round to two decimal places as needed) Za/2= Masind to him danimal minnndad\ Frequency 40- 30- 20- 10- - 0 4000 8000 12000 16000 20000 Salary (thousands of dollars) W

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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 90%, \( \sigma \) is not known, and the histogram of 65 player salaries (in thousands of dollars) of football players on a team is as shown:

**Histogram Explanation:**
- The histogram represents the distribution of salaries of 65 football players.
- The x-axis shows salary ranges in thousands of dollars, extending from 0 to 20,000.
- The y-axis indicates frequency, with the highest bar reaching approximately 40.
- The highest frequency occurs in the first salary range (0 to 4000 thousand dollars).
- As the salary range increases, the frequency of players in those ranges decreases significantly, showing a right-skewed distribution.

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

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

- \( \circ \) B. \( z_{\alpha/2} = \) ______ (Round to two decimal places as needed.)
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 90%, \( \sigma \) is not known, and the histogram of 65 player salaries (in thousands of dollars) of football players on a team is as shown: **Histogram Explanation:** - The histogram represents the distribution of salaries of 65 football players. - The x-axis shows salary ranges in thousands of dollars, extending from 0 to 20,000. - The y-axis indicates frequency, with the highest bar reaching approximately 40. - The highest frequency occurs in the first salary range (0 to 4000 thousand dollars). - As the salary range increases, the frequency of players in those ranges decreases significantly, showing a right-skewed distribution. **Select the correct choice below and, if necessary, fill in the answer box to complete your choice.** - \( \circ \) A. \( t_{\alpha/2} = \) ______ (Round to two decimal places as needed.) - \( \circ \) B. \( z_{\alpha/2} = \) ______ (Round to two decimal places as needed.)
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 90%, \( \sigma \) is not known, and the histogram of 65 player salaries (in thousands of dollars) of football players on a team is as shown.

**Options:**

- A: \( t_{\alpha/2} = \) [Textbox]  
  (Round to two decimal places as needed.)

- B: \( z_{\alpha/2} = \) [Textbox]  
  (Round to two decimal places as needed.)

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

**Graph Explanation:**

The histogram illustrates the distribution of salaries for 65 football players, measured in thousands of dollars. The horizontal axis represents the salary (ranging from 0 to 20,000) while the vertical axis represents the frequency of players falling into each salary range. 

- The first bar, representing salaries up to 4,000, is the tallest, with a frequency of about 35 players.
- Subsequent bars represent salary ranges of 4,000 increments, with significantly fewer players as the salary increases.
- The distribution is right-skewed, indicating that most players have lower salaries, with only a few earning toward the higher end.
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 90%, \( \sigma \) is not known, and the histogram of 65 player salaries (in thousands of dollars) of football players on a team is as shown. **Options:** - A: \( t_{\alpha/2} = \) [Textbox] (Round to two decimal places as needed.) - B: \( z_{\alpha/2} = \) [Textbox] (Round to two decimal places as needed.) - C: Neither the normal distribution nor the t distribution applies. **Graph Explanation:** The histogram illustrates the distribution of salaries for 65 football players, measured in thousands of dollars. The horizontal axis represents the salary (ranging from 0 to 20,000) while the vertical axis represents the frequency of players falling into each salary range. - The first bar, representing salaries up to 4,000, is the tallest, with a frequency of about 35 players. - Subsequent bars represent salary ranges of 4,000 increments, with significantly fewer players as the salary increases. - The distribution is right-skewed, indicating that most players have lower salaries, with only a few earning toward the higher end.
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