## 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 =