You are interested in finding a 90% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 10 randomly selected physical therapy patients. Round all answers to the nearest hundredth. 18 20 21 22 21 11 (a) = 17 (b) s = 17 (c) a = DNE 6 24 10 17 Enter DNE if this is unknown. Enter DNE if this is unknown. d) n = 10 e) Critical Value t Find the 90% confidence interval and complete the sentence below. onclusion: We estimate with 90 between and % confidence that the mean number of visits of physical therapy patients #texts.

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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### Understanding Confidence Intervals for Mean Number of Visits

This exercise involves calculating a 90% confidence interval for the mean number of visits to a physical therapist. The data below shows the number of visits for 10 randomly selected physical therapy patients. Follow the instructions to round all answers to the nearest hundredth.

#### Data:
- Visits: 18, 20, 21, 6, 24, 22, 21, 11, 10, 17

#### Steps:

1. **Calculate the Sample Mean (\(\bar{x}\))**:
   - \(\bar{x} = 17\)

2. **Sample Standard Deviation (\(s\))**:
   - \(s = 17\)
   - If unknown, calculate manually or it will be displayed as "DNE" (Does Not Exist).

3. **Population Standard Deviation (\(\sigma\))**:
   - \(\sigma\) is not directly provided and calculated as "DNE" if unknown.

4. **Sample Size (\(n\))**:
   - \(n = 10\)

5. **Critical Value (\(t\))**:
   - Use the \(t\)-distribution for a 90% confidence level.

6. **Find the Confidence Interval and Complete the Sentence**:
   - Determine the range for the mean number of visits with 90% confidence.
   - **Conclusion**: "We estimate with 90% confidence that the mean number of visits of physical therapy patients is between [lower bound] and [upper bound] visits."

### Conclusion

The task is to fill in the confidence interval values and complete the sentence to understand how confidence intervals can provide insight into the real-world application of statistical data in the medical field.
Transcribed Image Text:### Understanding Confidence Intervals for Mean Number of Visits This exercise involves calculating a 90% confidence interval for the mean number of visits to a physical therapist. The data below shows the number of visits for 10 randomly selected physical therapy patients. Follow the instructions to round all answers to the nearest hundredth. #### Data: - Visits: 18, 20, 21, 6, 24, 22, 21, 11, 10, 17 #### Steps: 1. **Calculate the Sample Mean (\(\bar{x}\))**: - \(\bar{x} = 17\) 2. **Sample Standard Deviation (\(s\))**: - \(s = 17\) - If unknown, calculate manually or it will be displayed as "DNE" (Does Not Exist). 3. **Population Standard Deviation (\(\sigma\))**: - \(\sigma\) is not directly provided and calculated as "DNE" if unknown. 4. **Sample Size (\(n\))**: - \(n = 10\) 5. **Critical Value (\(t\))**: - Use the \(t\)-distribution for a 90% confidence level. 6. **Find the Confidence Interval and Complete the Sentence**: - Determine the range for the mean number of visits with 90% confidence. - **Conclusion**: "We estimate with 90% confidence that the mean number of visits of physical therapy patients is between [lower bound] and [upper bound] visits." ### Conclusion The task is to fill in the confidence interval values and complete the sentence to understand how confidence intervals can provide insight into the real-world application of statistical data in the medical field.
Expert Solution
Step 1
  • Given data :

18,20,21,6,24,22,221,11,10,17

N=10

Df = n-1 = 9

Mean = (18+20+...17)/10 = 17

 

 

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