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) 17.598 Sx 16 01712719 n= 50 a. Express the confidence interval in the format that uses the "less than" symbol. Given that the original listed data use one decimal place, round the confidence interval limits accordingly O Mbps
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) 17.598 Sx 16 01712719 n= 50 a. Express the confidence interval in the format that uses the "less than" symbol. Given that the original listed data use one decimal place, round the confidence interval limits accordingly O Mbps
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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### Sample Question and Solution on Airport Data Speeds in Mbps
Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below.
#### Given Data:
- Confidence Interval (T Interval): (13.046, 22.15)
- Sample Mean (\( \bar{x} \)): 17.598
- Sample Standard Deviation (\( S_x \)): 16.01712719
- Sample Size (\( n \)): 50
---
#### a. Express the confidence interval in the format that uses the "less than" symbol. Given that the original listed data use one decimal place, round the confidence interval limits accordingly.
\[ \text{____ Mbps} < \mu < \text{____ Mbps} \]
**(Round to one decimal place as needed.)**
#### b. Identify the best point estimate of \( \mu \) and the margin of error.
- **Best Point Estimate of \( \mu \)**:
\[ \mu \approx \text{____ Mbps} \]
- **Margin of Error (\( E \))**:
\[ E = \text{____ Mbps} \]
**(Round to two decimal places as needed.)**
#### c. In constructing the confidence interval estimate of \( \mu \), why is it not necessary to confirm that the sample data appear to be from a population with a normal distribution?
- [ ] A. Because the sample is a random sample, the distribution of sample means can be treated as a normal distribution.
- [ ] B. Because the sample size of 50 is greater than 30, the distribution of sample means can be treated as a normal distribution.
- [ ] C. Because the sample standard deviation is known, the normal distribution can be used to construct the confidence interval.
- [ ] D. Because the population standard deviation is known, the normal distribution can be used to construct the confidence interval.
---
### Explanation of Accompanying Data Display:
**Graph/Diagram Details:**
- The data display provides the confidence interval (T interval), sample mean, sample standard deviation, and sample size.
- These values are essential in statistical analysis to estimate the population mean (\( \mu \)) with a specified level of confidence.
- The confidence interval is given as a range (13.046, 22.15) representing the plausible values for the population mean based on the sample data.
This](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6860f727-846a-4aef-a13d-345ae2e9be0e%2Fa05ad588-f3e8-4b0f-83bc-60656bf5a77f%2Fhgghq5e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Sample Question and Solution on Airport Data Speeds in Mbps
Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below.
#### Given Data:
- Confidence Interval (T Interval): (13.046, 22.15)
- Sample Mean (\( \bar{x} \)): 17.598
- Sample Standard Deviation (\( S_x \)): 16.01712719
- Sample Size (\( n \)): 50
---
#### a. Express the confidence interval in the format that uses the "less than" symbol. Given that the original listed data use one decimal place, round the confidence interval limits accordingly.
\[ \text{____ Mbps} < \mu < \text{____ Mbps} \]
**(Round to one decimal place as needed.)**
#### b. Identify the best point estimate of \( \mu \) and the margin of error.
- **Best Point Estimate of \( \mu \)**:
\[ \mu \approx \text{____ Mbps} \]
- **Margin of Error (\( E \))**:
\[ E = \text{____ Mbps} \]
**(Round to two decimal places as needed.)**
#### c. In constructing the confidence interval estimate of \( \mu \), why is it not necessary to confirm that the sample data appear to be from a population with a normal distribution?
- [ ] A. Because the sample is a random sample, the distribution of sample means can be treated as a normal distribution.
- [ ] B. Because the sample size of 50 is greater than 30, the distribution of sample means can be treated as a normal distribution.
- [ ] C. Because the sample standard deviation is known, the normal distribution can be used to construct the confidence interval.
- [ ] D. Because the population standard deviation is known, the normal distribution can be used to construct the confidence interval.
---
### Explanation of Accompanying Data Display:
**Graph/Diagram Details:**
- The data display provides the confidence interval (T interval), sample mean, sample standard deviation, and sample size.
- These values are essential in statistical analysis to estimate the population mean (\( \mu \)) with a specified level of confidence.
- The confidence interval is given as a range (13.046, 22.15) representing the plausible values for the population mean based on the sample data.
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