Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below. Mbps<μ< Mbps (Round to two decimal places as needed.) b. Identify the best point estimate of μ and the margin of error. 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. The point estimate of μ is Mbps. (Round to two decimal places as needed.) Tinterval The margin of error is E = Mbps. (Round to two decimal places as needed.) (13.046,22.15) x= 17.598 Sx= 16.01712719 n = 50 c. In constructing the confidence interval estimate of μ, why is it not necessary to confirm that the sample data appear to be from a population with a normal distribution? O A. Because the sample standard deviation is known, the normal distribution can be used to construct the confidence interval. 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 population standard deviation is known, the normal distribution can be used to construct the confidence interval. O D. Because the sample is a random sample, the distribution of sample means can be treated as a normal distribution.
Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below. Mbps<μ< Mbps (Round to two decimal places as needed.) b. Identify the best point estimate of μ and the margin of error. 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. The point estimate of μ is Mbps. (Round to two decimal places as needed.) Tinterval The margin of error is E = Mbps. (Round to two decimal places as needed.) (13.046,22.15) x= 17.598 Sx= 16.01712719 n = 50 c. In constructing the confidence interval estimate of μ, why is it not necessary to confirm that the sample data appear to be from a population with a normal distribution? O A. Because the sample standard deviation is known, the normal distribution can be used to construct the confidence interval. 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 population standard deviation is known, the normal distribution can be used to construct the confidence interval. O D. Because the sample is a random sample, the distribution of sample means can be treated as a normal distribution.
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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![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)
x̄ = 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.
\[ \text{Mbps} < \mu < \text{Mbps} \]
(Round to two decimal places as needed.)
**b. Identify the best point estimate of μ and the margin of error.**
- The point estimate of μ is \[ \] Mbps.
(Round to two decimal places as needed.)
- The margin of error is E = \[ \] Mbps.
(Round to two decimal places as needed.)
**c. In constructing the confidence interval estimate of μ, 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 standard deviation is known, the normal distribution can be used to construct the confidence interval.
- ○ 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 population standard deviation is known, the normal distribution can be used to construct the confidence interval.
- ○ D. Because the sample is a random sample, the distribution of sample means can be treated as a normal distribution.
---
**Explanation:**
- **Data Summary:**
- Confidence interval range: (13.046, 22.15)
- Sample mean (x̄): 17.598 Mbps
- Sample standard deviation (Sx): 16.01712719 Mbps
- Sample size (n): 50
This analysis calculates a confidence interval for the average data speeds at airports, based on the sample data provided. By using these calculations, one can estimate the range within which the true mean speed (μ) lies with a certain level of confidence. The options provided help determine the reason for assuming a normal distribution of the sample means, particularly given the sample size.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7038cbde-5259-4f1b-ade8-fa8f6320a6eb%2F6e00f711-d8fc-4f30-815d-735af5f8ae2c%2Fspl9nr_processed.png&w=3840&q=75)
Transcribed Image Text: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)
x̄ = 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.
\[ \text{Mbps} < \mu < \text{Mbps} \]
(Round to two decimal places as needed.)
**b. Identify the best point estimate of μ and the margin of error.**
- The point estimate of μ is \[ \] Mbps.
(Round to two decimal places as needed.)
- The margin of error is E = \[ \] Mbps.
(Round to two decimal places as needed.)
**c. In constructing the confidence interval estimate of μ, 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 standard deviation is known, the normal distribution can be used to construct the confidence interval.
- ○ 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 population standard deviation is known, the normal distribution can be used to construct the confidence interval.
- ○ D. Because the sample is a random sample, the distribution of sample means can be treated as a normal distribution.
---
**Explanation:**
- **Data Summary:**
- Confidence interval range: (13.046, 22.15)
- Sample mean (x̄): 17.598 Mbps
- Sample standard deviation (Sx): 16.01712719 Mbps
- Sample size (n): 50
This analysis calculates a confidence interval for the average data speeds at airports, based on the sample data provided. By using these calculations, one can estimate the range within which the true mean speed (μ) lies with a certain level of confidence. The options provided help determine the reason for assuming a normal distribution of the sample means, particularly given the sample size.
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