A random sample of 25 items is drawn from a population whose standard deviation is unknown. The sample mean is = 850 and the sample standard deviation is s= 15. Use Appendix D to find the values of Student's t. (a) Construct an interval estimate of u with 95% confidence. (Round your answers to 3 decimal places.) The 95% confidence interval is from to (b) Construct an interval estimate of u with 95% confidence, assuming that s 30. (Round your answers to 3 decimal places.) The 95% confidence interval is from to (c) Construct an interval estimate of u with 95% confidence, assuming that s= 60. (Round your answers to 3 decimal places.) The 95% confidence interval is from to (d) Describe how the confidence interval changes as s increases.

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A random sample of 25 items is drawn from a population whose standard deviation is unknown. The sample mean is \( \bar{x} = 850 \) and the sample standard deviation is \( s = 15 \). Use Appendix D to find the values of Student’s \( t \).

(a) Construct an interval estimate of \( \mu \) with 95% confidence. **(Round your answers to 3 decimal places.)**

The 95% confidence interval is from [______] to [______].

(b) Construct an interval estimate of \( \mu \) with 95% confidence, assuming that \( s = 30 \). **(Round your answers to 3 decimal places.)**

The 95% confidence interval is from [______] to [______].

(c) Construct an interval estimate of \( \mu \) with 95% confidence, assuming that \( s = 60 \). **(Round your answers to 3 decimal places.)**

The 95% 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.
Transcribed Image Text:A random sample of 25 items is drawn from a population whose standard deviation is unknown. The sample mean is \( \bar{x} = 850 \) and the sample standard deviation is \( s = 15 \). Use Appendix D to find the values of Student’s \( t \). (a) Construct an interval estimate of \( \mu \) with 95% confidence. **(Round your answers to 3 decimal places.)** The 95% confidence interval is from [______] to [______]. (b) Construct an interval estimate of \( \mu \) with 95% confidence, assuming that \( s = 30 \). **(Round your answers to 3 decimal places.)** The 95% confidence interval is from [______] to [______]. (c) Construct an interval estimate of \( \mu \) with 95% confidence, assuming that \( s = 60 \). **(Round your answers to 3 decimal places.)** The 95% 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.
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