Use the sample information= 40, 0 = 3, n= 13 to calculate the following confidence intervals for p 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 to (b) 95 percent confidence. (Round your answers to 4 decimal places.) The 95% confidence interval is from to (c) 99 percent confidence. (Round your answers to 4 decimal places.) The 99% confidence interval is from to (d) Describe how the intervals change as you increase the confidence level. O The interval gets narrower as the confidence level increases. O The interval gets wider as the confidence level decreases. O The interval gets wider as the confidence level increases. O The interval stays the same as the confidence level increases.

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### Calculating Confidence Intervals

Use the sample information \( \bar{x} = 40, \sigma = 3, n = 13 \) 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 \[ \_\_\_\_\_ \] to \[ \_\_\_\_\_ \].

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

The 95% confidence interval is from \[ \_\_\_\_\_ \] to \[ \_\_\_\_\_ \].

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

The 99% confidence interval is from \[ \_\_\_\_\_ \] to \[ \_\_\_\_\_ \].

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

- \( \bigcirc \) The interval gets narrower as the confidence level increases.
- \( \bigcirc \) The interval gets wider as the confidence level decreases.
- \( \bigcirc \) The interval gets wider as the confidence level increases.
- \( \bigcirc \) The interval stays the same as the confidence level increases.
Transcribed Image Text:### Calculating Confidence Intervals Use the sample information \( \bar{x} = 40, \sigma = 3, n = 13 \) 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 \[ \_\_\_\_\_ \] to \[ \_\_\_\_\_ \]. #### (b) 95 percent confidence **(Round your answers to 4 decimal places.)** The 95% confidence interval is from \[ \_\_\_\_\_ \] to \[ \_\_\_\_\_ \]. #### (c) 99 percent confidence **(Round your answers to 4 decimal places.)** The 99% confidence interval is from \[ \_\_\_\_\_ \] to \[ \_\_\_\_\_ \]. #### (d) Describe how the intervals change as you increase the confidence level. - \( \bigcirc \) The interval gets narrower as the confidence level increases. - \( \bigcirc \) The interval gets wider as the confidence level decreases. - \( \bigcirc \) The interval gets wider as the confidence level increases. - \( \bigcirc \) The interval stays the same as the confidence level increases.
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