Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below, TInterval (13.046,22.15) x = 17.598 E Click the icon to view a t distribution table. Sx = 16.01712719 n= 50 a. What is the number of degrees of freedom that should be used for finding the critical value t,12? df = (Type a whole number.) b. Find the critical value t/2 corresponding to a 95% confidence level. ta/2=0 (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 number of sample values that are determined after certain restrictions have been imposed on all data values. B. The number of degrees of freedom for a collection of sample data is the total number of sample values. OC. The number of degrees of freedom for a collection of sample data is the number of unique, non-repeated sample values. D. 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. OO O

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**Educational Content: Understanding Degrees of Freedom in Statistical Analysis**

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

- **Click the icon** to view a t distribution table.

### Task Requirements

#### a. Calculate the Degrees of Freedom

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. Determine the Critical Value

Find the critical value \( t_{\alpha/2} \) corresponding to a 95% confidence level.

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

#### c. Describe Degrees of Freedom

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

- **Option A:** 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.
- **Option B:** The number of degrees of freedom for a collection of sample data is the total number of sample values.
- **Option C:** The number of degrees of freedom for a collection of sample data is the number of unique, non-repeated sample values.
- **Option D:** 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.

**Click to select your answer(s).**

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### Data Summary

- **Confidence Interval (T Interval):** \((13.046, 22.15)\)
- **Sample Mean (\(x\)) =** 17.598
- **Sample Standard Deviation (\(Sx\)) =** 16.01712719
- **Sample Size (\(n\)) =** 50

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This content helps you understand how to calculate degrees of freedom, find critical values for confidence intervals, and comprehend the concept of degrees of freedom in statistics.
Transcribed Image Text:**Educational Content: Understanding Degrees of Freedom in Statistical Analysis** --- Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below. - **Click the icon** to view a t distribution table. ### Task Requirements #### a. Calculate the Degrees of Freedom 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. Determine the Critical Value Find the critical value \( t_{\alpha/2} \) corresponding to a 95% confidence level. - \( t_{\alpha/2} = \) [______] *(Round to two decimal places as needed.)* #### c. Describe Degrees of Freedom Give a brief general description of the number of degrees of freedom. - **Option A:** 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. - **Option B:** The number of degrees of freedom for a collection of sample data is the total number of sample values. - **Option C:** The number of degrees of freedom for a collection of sample data is the number of unique, non-repeated sample values. - **Option D:** 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. **Click to select your answer(s).** --- ### Data Summary - **Confidence Interval (T Interval):** \((13.046, 22.15)\) - **Sample Mean (\(x\)) =** 17.598 - **Sample Standard Deviation (\(Sx\)) =** 16.01712719 - **Sample Size (\(n\)) =** 50 --- This content helps you understand how to calculate degrees of freedom, find critical values for confidence intervals, and comprehend the concept of degrees of freedom in statistics.
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