A simple random sample with n = 58 provided a sample mean of 23.5 and a sample standard deviation of 4.4. (Round your answers to one decimal place.) (a) Develop a 90% confidence interval for the population mean. 23.6 to 23.4 (b) Develop a 95% confidence interval for the population mean. to (c) Develop a 99% confidence interval for the population mean. to (d) What happens to the margin of error and the confidence interval as the confidence level is increased? O As the confidence level increases, there is a smaller margin of error and a wider confidence interval. O As the confidence level increases, there is a smaller margin of error and a more narrow confidence interval. As the confidence level increases, there is a larger margin of error and a more narrow confidence interval. As the confidence level increases, there is a larger margin of error and a wider confidence interval.

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**Confidence Interval and Margin of Error**

You may need to use the appropriate appendix table or technology to answer this question.

A simple random sample with \( n = 58 \) provided a sample mean of \( 23.5 \) and a sample standard deviation of \( 4.4 \). (Round your answers to one decimal place.)

**(a)** Develop a 90% confidence interval for the population mean.

\[ 23.6 \text{ to } 23.4 \]

**(b)** Develop a 95% confidence interval for the population mean.

\[ \_\_\_ \text{ to } \_\_\_ \]

**(c)** Develop a 99% confidence interval for the population mean.

\[ \_\_\_ \text{ to } \_\_\_ \]

**(d)** What happens to the margin of error and the confidence interval as the confidence level is increased?

- \( \bigcirc \) As the confidence level increases, there is a smaller margin of error and a wider confidence interval.
- \( \bigcirc \) As the confidence level increases, there is a smaller margin of error and a more narrow confidence interval.
- \( \bigcirc \) As the confidence level increases, there is a larger margin of error and a more narrow confidence interval.
- \( \bigcirc \) As the confidence level increases, there is a larger margin of error and a wider confidence interval.
Transcribed Image Text:**Confidence Interval and Margin of Error** You may need to use the appropriate appendix table or technology to answer this question. A simple random sample with \( n = 58 \) provided a sample mean of \( 23.5 \) and a sample standard deviation of \( 4.4 \). (Round your answers to one decimal place.) **(a)** Develop a 90% confidence interval for the population mean. \[ 23.6 \text{ to } 23.4 \] **(b)** Develop a 95% confidence interval for the population mean. \[ \_\_\_ \text{ to } \_\_\_ \] **(c)** Develop a 99% confidence interval for the population mean. \[ \_\_\_ \text{ to } \_\_\_ \] **(d)** What happens to the margin of error and the confidence interval as the confidence level is increased? - \( \bigcirc \) As the confidence level increases, there is a smaller margin of error and a wider confidence interval. - \( \bigcirc \) As the confidence level increases, there is a smaller margin of error and a more narrow confidence interval. - \( \bigcirc \) As the confidence level increases, there is a larger margin of error and a more narrow confidence interval. - \( \bigcirc \) As the confidence level increases, there is a larger margin of error and a wider confidence interval.
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