Use the standard normal distribution or the t-distribution O construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 41 people, the mean body mass index (BMI) was 28.1 and the standard deviation was 6.21. Which distribution should be used to construct the confidence interval? Choose the correct answer below. OA. Use a normal distribution because the sample is random, n ≥ 30, and a is known. OB. Use a t-distribution because the sample random, n ≥ 30, and a is unknown. OC. Use a normal distribution because the sample is random, the population is normal, and a is known. OD. Use a t-distribution because the sample. random, the population is normal, and a is unknown. OE. Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or n<30, and the population is not known to be normal. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. OA. The 95% confidence interval is (.1). (Round to two decimal places as needed.) OB. Neither distribution can be used to construct the confidence interval. Interpret the results. Choose the correct answer below. O A. With 95% confidence, it can be said that the population mean BMI is between the bounds of the confidence interval. OB. It can be said that 95% of people have a BMI between the bounds of the confidence interval. OC. If a large sample of people are taken approximately 95% of them will have a BMI between the bounds of the confidence interval. OD. Neither distribution can be used to construct the confidence interval.
Use the standard normal distribution or the t-distribution O construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 41 people, the mean body mass index (BMI) was 28.1 and the standard deviation was 6.21. Which distribution should be used to construct the confidence interval? Choose the correct answer below. OA. Use a normal distribution because the sample is random, n ≥ 30, and a is known. OB. Use a t-distribution because the sample random, n ≥ 30, and a is unknown. OC. Use a normal distribution because the sample is random, the population is normal, and a is known. OD. Use a t-distribution because the sample. random, the population is normal, and a is unknown. OE. Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or n<30, and the population is not known to be normal. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. OA. The 95% confidence interval is (.1). (Round to two decimal places as needed.) OB. Neither distribution can be used to construct the confidence interval. Interpret the results. Choose the correct answer below. O A. With 95% confidence, it can be said that the population mean BMI is between the bounds of the confidence interval. OB. It can be said that 95% of people have a BMI between the bounds of the confidence interval. OC. If a large sample of people are taken approximately 95% of them will have a BMI between the bounds of the confidence interval. OD. Neither distribution can be used to construct the confidence interval.
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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![### Constructing a 95% Confidence Interval for the Population Mean
Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results.
In a random sample of 41 people, the mean Body Mass Index (BMI) was 28.1 and the standard deviation was 6.21.
---
### Which distribution should be used to construct the confidence interval?
Choose the correct answer below:
- **A.** Use a normal distribution because the sample is random, n ≥ 30, and σ is known.
- **B.** Use a t-distribution because the sample is random, n ≥ 30, and σ is unknown.
- **C.** Use a normal distribution because the sample is random, the population is normal, and σ is known.
- **D.** Use a t-distribution because the sample is random, the population is normal, and σ is unknown.
- **E.** Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or n < 30, and the population is not known to be normal.
---
### Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice:
- **A.** The 95% confidence interval is [_____, _____].
*(Round to two decimal places as needed.)*
- **B.** Neither distribution can be used to construct the confidence interval.
---
### Interpret the results.
Choose the correct answer below:
- **A.** With 95% confidence, it can be said that the population mean BMI is between the bounds of the confidence interval.
- **B.** It can be said that 95% of people have a BMI between the bounds of the confidence interval.
- **C.** If a large sample of people are taken approximately 95% of them will have a BMI between the bounds of the confidence interval.
- **D.** Neither distribution can be used to construct the confidence interval.
---
By understanding the specific conditions and the methodology required to construct a 95% confidence interval, you can better interpret the statistical meaning and implications of your data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac4255ba-2787-4b8b-b63d-664d949df058%2F9e97856b-45d2-49ec-8311-b8f4fe5b6026%2Fc1fja2w_processed.png&w=3840&q=75)
Transcribed Image Text:### Constructing a 95% Confidence Interval for the Population Mean
Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results.
In a random sample of 41 people, the mean Body Mass Index (BMI) was 28.1 and the standard deviation was 6.21.
---
### Which distribution should be used to construct the confidence interval?
Choose the correct answer below:
- **A.** Use a normal distribution because the sample is random, n ≥ 30, and σ is known.
- **B.** Use a t-distribution because the sample is random, n ≥ 30, and σ is unknown.
- **C.** Use a normal distribution because the sample is random, the population is normal, and σ is known.
- **D.** Use a t-distribution because the sample is random, the population is normal, and σ is unknown.
- **E.** Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or n < 30, and the population is not known to be normal.
---
### Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice:
- **A.** The 95% confidence interval is [_____, _____].
*(Round to two decimal places as needed.)*
- **B.** Neither distribution can be used to construct the confidence interval.
---
### Interpret the results.
Choose the correct answer below:
- **A.** With 95% confidence, it can be said that the population mean BMI is between the bounds of the confidence interval.
- **B.** It can be said that 95% of people have a BMI between the bounds of the confidence interval.
- **C.** If a large sample of people are taken approximately 95% of them will have a BMI between the bounds of the confidence interval.
- **D.** Neither distribution can be used to construct the confidence interval.
---
By understanding the specific conditions and the methodology required to construct a 95% confidence interval, you can better interpret the statistical meaning and implications of your data.
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