Question

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 =

Answer 1

x̅ = 3.8711

Confidence interval = 95%

At α = 1-0.95 = 0.05, two tailed critical value, z_c = NORM.S.INV(0.05/ 2) = 1.96

Margin of error, E= z_c* σ_x = 1.96 * 0.1704 = 0.3340

95% Confidence interval :

Lower Bound = x̅ - E = 3.8711- 0.3340 = 3.5371

Upper Bound = x̅ + E = 3.8711+ 0.3340 = 4.2051