MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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.
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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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