Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below. TInterva E Click the icon to view at distribution table. (13.046,22.15) X= 17.598 Sx = 16.01712719 n= 50 a. What is the number of degrees of freedom that should be used for finding the critical value t2? df =O (Type a whole number.) b. Find the critical value t2 corresponding to a 95% confidence level. (Round to two decimal places as needed.) c. Give a brief general description of the number of degrees of freedom. O A. The number of degrees of freedom for a collection of sample data is the total number sample values. O B. The number of degrees of freedom for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values. OC. The number of degrees of freedom for a collection of sample data is the number of sample values that are determined after certain restrictions have been imposed on all data values. O D. The number of degrees of freedom for a collection of sample data is the number of unique, non-repeated sample values.

Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below. TInterva E Click the icon to view at distribution table. (13.046,22.15) X= 17.598 Sx = 16.01712719 n= 50 a. What is the number of degrees of freedom that should be used for finding the critical value t2? df =O (Type a whole number.) b. Find the critical value t2 corresponding to a 95% confidence level. (Round to two decimal places as needed.) c. Give a brief general description of the number of degrees of freedom. O A. The number of degrees of freedom for a collection of sample data is the total number sample values. O B. The number of degrees of freedom for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values. OC. The number of degrees of freedom for a collection of sample data is the number of sample values that are determined after certain restrictions have been imposed on all data values. O D. The number of degrees of freedom for a collection of sample data is the number of unique, non-repeated sample values.

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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Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

**Educational Website Transcription**

Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below.

**Data Summary:**
- **TInterval:** $ (13.046, 22.15) $
- **Sample Mean ($ x̄ $):** 17.598
- **Sample Standard Deviation ($ Sx $):** 16.01712719
- **Sample Size ($ n $):** 50

**Tasks:**

a. **What is the number of degrees of freedom that should be used for finding the critical value $ t_{\alpha/2} $?**

- **df =** (Type a whole number.)

b. **Find the critical value $ t_{\alpha/2} $ corresponding to a 95% confidence level.**

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

c. **Give a brief general description of the number of degrees of freedom.**

- **Options:**
- **A.** The number of degrees of freedom for a collection of sample data is the total number of sample values.
- **B.** The number of degrees of freedom for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.
- **C.** The number of degrees of freedom for a collection of sample data is the number of sample values that are determined after certain restrictions have been imposed on all data values.
- **D.** The number of degrees of freedom for a collection of sample data is the number of unique, non-repeated sample values.

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 99%, $ \sigma = 4095 $ thousand dollars, and the histogram of 64 player salaries (in thousands of dollars) of football players on a team is as shown.

### Graph Description:
The histogram represents the frequency of player salaries in thousands of dollars. It exhibits a right-skewed distribution, with most of the salaries clustered between 0 and 4000 thousand dollars.

#### Histogram Details:
- X-axis: Salary (thousands of dollars)
- Y-axis: Frequency
- The first bar, representing salaries from 0 to 4000 thousand dollars, is the tallest, indicating the highest frequency.

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

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

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

- $ \bigcirc $ C. Neither the normal distribution nor the t distribution applies.

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