Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical valuetα/2,(b) find the critical valuezα/2,or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is95%,σ=3473thousand dollars, and the histogram of56player salaries (in thousands of dollars) of football players on a team is as shown. 040008000120001600020000010203040Salary (thousands of dollars)Frequency Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A.tα/2=(Round to two decimal places as needed.) B.zα/2=(Round to two decimal places as needed.) C.Neither the normal distribution nor the t distribution applies. **Constructing a Confidence Interval**Assume we want to construct a confidence interval. Perform one of the following actions, as appropriate: (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 confidence level is 95%, $ \sigma = 3473 $ thousand dollars, and the histogram of 56 player salaries (in thousands of dollars) of football players on a team is displayed as follows:**Histogram Details:**- The histogram shows the distribution of salaries of 56 football players.- Salary (in thousands of dollars) is on the x-axis, ranging from 0 to 20,000.- Frequency is on the y-axis, ranging from 0 to 40.- Most players have salaries between 0 and 4,000 thousand dollars, with the highest frequency close to 40.- A few players have salaries extending beyond 4,000 thousand dollars, with frequencies decreasing as salaries increase, reaching nearly zero for salaries above 16,000 thousand dollars.**Select the correct option and, if needed, fill in the answer box to complete your choice:**- **A.** $ t_{\alpha/2} = $ [ ] - *(Round to two decimal places as needed.)*- **B.** $ z_{\alpha/2} = $ [ ] - *(Round to two decimal places as needed.)*- **C.** ☑ Neither the normal distribution nor the t distribution applies.*(In this scenario, option C is selected because the data may not meet criteria for using normal or t distribution models due to skewness or other factors.)*

Solution: From the given information, the confidence level is 0.95 and σ=3473 thousand dollars.

Answered: Assume that we want to construct a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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

tα/2,

(b) find the critical value

zα/2,

or (c) state that neither the normal distribution nor the t distribution applies.

The confidence level is

95%,

σ=3473

thousand dollars, and the histogram of

player salaries (in thousands of dollars) of football players on a team is as shown.

040008000120001600020000010203040Salary (thousands of dollars)Frequency

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

tα/2=

(Round to two decimal places as needed.)

zα/2=

(Round to two decimal places as needed.)

Neither the normal distribution nor the t distribution applies.

**Constructing a Confidence Interval**

Assume we want to construct a confidence interval. Perform one of the following actions, as appropriate:

(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 confidence level is 95%, $ \sigma = 3473 $ thousand dollars, and the histogram of 56 player salaries (in thousands of dollars) of football players on a team is displayed as follows:

**Histogram Details:**

- The histogram shows the distribution of salaries of 56 football players.
- Salary (in thousands of dollars) is on the x-axis, ranging from 0 to 20,000.
- Frequency is on the y-axis, ranging from 0 to 40.
- Most players have salaries between 0 and 4,000 thousand dollars, with the highest frequency close to 40.
- A few players have salaries extending beyond 4,000 thousand dollars, with frequencies decreasing as salaries increase, reaching nearly zero for salaries above 16,000 thousand dollars.

**Select the correct option and, if needed, fill in the answer box to complete your choice:**

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

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

- **C.** ☑ Neither the normal distribution nor the t distribution applies.

*(In this scenario, option C is selected because the data may not meet criteria for using normal or t distribution models due to skewness or other factors.)*

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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