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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 to/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 90%, o=4128 thousand dollars, and the histogram of 60 player salaries (in thousands of dollars) of football players on a team is as shown. Frequency

Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value to/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 90%, o=4128 thousand dollars, and the histogram of 60 player salaries (in thousands of dollars) of football players on a team is as shown. Frequency

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Confidence Interval Construction **Scenario:** We aim to construct a confidence interval. The task is to either: - (a) Find the critical value \( t_{\alpha/2} \) - (b) Find the critical value \( z_{\alpha/2} \) - (c) State that neither the normal distribution nor the t distribution applies. The parameters are as follows: - **Confidence Level:** 90% - **Standard Deviation (\( \sigma \))**: 4128 thousand dollars - **Sample Size:** 60 football players - **Data Representation:** Histogram of 60 player salaries (in thousands of dollars) **Histogram Details:** The histogram provided represents the salaries of football players: - X-axis: Salary (in thousands of dollars) - Y-axis: Frequency The histogram indicates a right-skewed distribution of salaries, with most values clustered at lower salary ranges and a few extending to higher amounts. **Options for Critical Value Selection:** Choose the correct answer and, if required, complete the value in the answer box: - **Option A: \( t_{\alpha/2} = \)** - (Round to two decimal places as needed.) - **Option B: \( z_{\alpha/2} = \)** - (Round to two decimal places as needed.) - **Option C:** Neither the normal distribution nor the t distribution applies. --- *Note: Accurate determination relies on understanding the distribution and sample size context. Attention must be given to the need for corresponding critical values based on whether the underlying distribution aligns with normality or a t-distribution.* --- **Graph Interpretation:** The histogram shows a skewed distribution, suggesting that salaries are not normally distributed. This would typically impact the approach taken to compute confidence intervals, and might influence whether option (a) or (c) is more appropriate.
Transcribed Image Text:### Confidence Interval Construction **Scenario:** We aim to construct a confidence interval. The task is to either: - (a) Find the critical value \( t_{\alpha/2} \) - (b) Find the critical value \( z_{\alpha/2} \) - (c) State that neither the normal distribution nor the t distribution applies. The parameters are as follows: - **Confidence Level:** 90% - **Standard Deviation (\( \sigma \))**: 4128 thousand dollars - **Sample Size:** 60 football players - **Data Representation:** Histogram of 60 player salaries (in thousands of dollars) **Histogram Details:** The histogram provided represents the salaries of football players: - X-axis: Salary (in thousands of dollars) - Y-axis: Frequency The histogram indicates a right-skewed distribution of salaries, with most values clustered at lower salary ranges and a few extending to higher amounts. **Options for Critical Value Selection:** Choose the correct answer and, if required, complete the value in the answer box: - **Option A: \( t_{\alpha/2} = \)** - (Round to two decimal places as needed.) - **Option B: \( z_{\alpha/2} = \)** - (Round to two decimal places as needed.) - **Option C:** Neither the normal distribution nor the t distribution applies. --- *Note: Accurate determination relies on understanding the distribution and sample size context. Attention must be given to the need for corresponding critical values based on whether the underlying distribution aligns with normality or a t-distribution.* --- **Graph Interpretation:** The histogram shows a skewed distribution, suggesting that salaries are not normally distributed. This would typically impact the approach taken to compute confidence intervals, and might influence whether option (a) or (c) is more appropriate.
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