A random sample of 23 items is drawn from a population whose standard deviation is unknown. The sample mean is = 820 and the sample standard deviation is s= 25. Use Appendix D to find the values of Student's t (a) Construct an interval estimate of u with 99% confidence. (Round your answers to 3 decimal places.) The 99% confidence interval is from to (b) Construct an interval estimate of u with 99% confidence, assuming that s= 50. (Round your answers to 3 decimal places.) The 99% confidence interval is from (c) Construct an interval estimate of u with 99% confidence, assuming that s = 100. (Round your answers to 3 decimal places.) The 99% confidence interval is from to (d) Describe how the confidence interval changes as s increases. O The interval stays the same as s increases. es O The interval gets wider as s increases. O The interval gets narrower as s increases.

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**Chapter 8 Homework: Confidence Intervals**

A random sample of 23 items is drawn from a population whose standard deviation is unknown. The sample mean is \( \bar{x} = 820 \) and the sample standard deviation is \( s = 25 \). Use [Appendix D](#) to find the values of Student's t.

(a) Construct an interval estimate of \( \mu \) with 99% confidence. (Round your answers to 3 decimal places.)

The 99% confidence interval is from [______] to [______].

(b) Construct an interval estimate of \( \mu \) with 99% confidence, assuming that \( s = 50 \). (Round your answers to 3 decimal places.)

The 99% confidence interval is from [______] to [______].

(c) Construct an interval estimate of \( \mu \) with 99% confidence, assuming that \( s = 100 \). (Round your answers to 3 decimal places.)

The 99% confidence interval is from [______] to [______].

(d) Describe how the confidence interval changes as \( s \) increases.

- The interval stays the same as \( s \) increases.
- The interval gets wider as \( s \) increases.
- The interval gets narrower as \( s \) increases.

**Please refer to Appendix D for the values of Student's t needed to complete the calculations.**
Transcribed Image Text:**Chapter 8 Homework: Confidence Intervals** A random sample of 23 items is drawn from a population whose standard deviation is unknown. The sample mean is \( \bar{x} = 820 \) and the sample standard deviation is \( s = 25 \). Use [Appendix D](#) to find the values of Student's t. (a) Construct an interval estimate of \( \mu \) with 99% confidence. (Round your answers to 3 decimal places.) The 99% confidence interval is from [______] to [______]. (b) Construct an interval estimate of \( \mu \) with 99% confidence, assuming that \( s = 50 \). (Round your answers to 3 decimal places.) The 99% confidence interval is from [______] to [______]. (c) Construct an interval estimate of \( \mu \) with 99% confidence, assuming that \( s = 100 \). (Round your answers to 3 decimal places.) The 99% confidence interval is from [______] to [______]. (d) Describe how the confidence interval changes as \( s \) increases. - The interval stays the same as \( s \) increases. - The interval gets wider as \( s \) increases. - The interval gets narrower as \( s \) increases. **Please refer to Appendix D for the values of Student's t needed to complete the calculations.**
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