A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 104, and the sample standard deviation, s, is found to be 8. (a) Construct a 95% confidence interval about u if the sample size, n, is 22. (b) Construct a 95% confidence interval about u if the sample size, n, is 16. (c) Construct a 90% confidence interval about u if the sample size, n, is 22. (d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed? (a) Construct a 95% confidence interval about u if the sample size, n, is 22. Lower bound: ; Upper bound: (Round to one decimal place as needed.)

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A simple random sample of size \( n \) is drawn from a population that is normally distributed. The sample mean, \( \bar{x} \), is found to be 104, and the sample standard deviation, \( s \), is found to be 8.

(a) Construct a 95% confidence interval about \( \mu \) if the sample size, \( n \), is 22.

(b) Construct a 95% confidence interval about \( \mu \) if the sample size, \( n \), is 16.

(c) Construct a 90% confidence interval about \( \mu \) if the sample size, \( n \), is 22.

(d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed?

---

(a) Construct a 95% confidence interval about \( \mu \) if the sample size, \( n \), is 22.

- Lower bound: \[ \boxed{} \]
- Upper bound: \[ \boxed{} \]

(Round to one decimal place as needed.)
Transcribed Image Text:A simple random sample of size \( n \) is drawn from a population that is normally distributed. The sample mean, \( \bar{x} \), is found to be 104, and the sample standard deviation, \( s \), is found to be 8. (a) Construct a 95% confidence interval about \( \mu \) if the sample size, \( n \), is 22. (b) Construct a 95% confidence interval about \( \mu \) if the sample size, \( n \), is 16. (c) Construct a 90% confidence interval about \( \mu \) if the sample size, \( n \), is 22. (d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed? --- (a) Construct a 95% confidence interval about \( \mu \) if the sample size, \( n \), is 22. - Lower bound: \[ \boxed{} \] - Upper bound: \[ \boxed{} \] (Round to one decimal place as needed.)
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