## Suppose the math department chair at a large state university wants to estimate the average overall…

Suppose the math department chair at a large state university

wants to estimate the average overall rating, out of five points,

that students taking Introductory Statistics gave their lecturers

on their end-of-term evaluations. She selects a random sample of 36

evaluations and records the summary statistics shown.

Sample size | Sample mean | Sample standard deviation | Population standard deviation | Standard deviation of ?¯ | Confidence level |
---|---|---|---|---|---|

? | ?⎯⎯⎯ | ? | ? | ??⎯⎯⎯⎯ | ? |

36 | 3.8711 | 1.0755 | 1.0222 | 0.1704 | 95% |

The department chair determines the standard deviation of the

sampling distribution of ?⎯⎯⎯ using ?, the standard deviation

calculated from all student evaluations submitted to her

department. Assume the Statistics lecturers’ ratings have the same

standard deviation.

Use this information to find the margin of error and the lower

and upper limits of a 95% confidence interval for ?, the mean

overall rating students gave their Introductory Statistics

lecturers. Round your answers to the nearest hundredth.

Complete the following sentence to state the interpretation of

the department chair’s confidence interval.

Margin of error =