Use the sample information = 36, 0 = 7, n= 16 to calculate the following confidence intervals for u assuming the sample is ormal population. ) 90 percent confidence. (Round your answers to 4 decimal places.) The 90% confidence interval is from 33.1213 to 38.8788 b) 95 percent confidence. (Round your answers to 4 decimal places.) The 95% confidence interval is from 32.57 to 39.43 c) 99 percent confidence. (Round your answers to 4 decimal places.) The 99% confidence interval is from to

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Use the sample information \( \bar{x} = 36, \sigma = 7, n = 16 \) to calculate the following confidence intervals for \(\mu\) assuming the sample is from a normal population.

**(a)** 90 percent confidence. *(Round your answers to 4 decimal places.)*

The 90% confidence interval is from \([33.1213, 38.8788]\).

**(b)** 95 percent confidence. *(Round your answers to 4 decimal places.)*

The 95% confidence interval is from \([32.57, 39.43]\).

**(c)** 99 percent confidence. *(Round your answers to 4 decimal places.)*

The 99% confidence interval is from \([\_\_\_\_, \_\_\_\_]\).

**(d)** Describe how the intervals change as you increase the confidence level.

- ☐ The interval gets narrower as the confidence level increases.
- ☐ The interval gets wider as the confidence level decreases.
- ☑ The interval gets wider as the confidence level increases.
- ☐ The interval stays the same as the confidence level increases.
Transcribed Image Text:Use the sample information \( \bar{x} = 36, \sigma = 7, n = 16 \) to calculate the following confidence intervals for \(\mu\) assuming the sample is from a normal population. **(a)** 90 percent confidence. *(Round your answers to 4 decimal places.)* The 90% confidence interval is from \([33.1213, 38.8788]\). **(b)** 95 percent confidence. *(Round your answers to 4 decimal places.)* The 95% confidence interval is from \([32.57, 39.43]\). **(c)** 99 percent confidence. *(Round your answers to 4 decimal places.)* The 99% confidence interval is from \([\_\_\_\_, \_\_\_\_]\). **(d)** Describe how the intervals change as you increase the confidence level. - ☐ The interval gets narrower as the confidence level increases. - ☐ The interval gets wider as the confidence level decreases. - ☑ The interval gets wider as the confidence level increases. - ☐ The interval stays the same as the confidence level increases.
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