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 38 evaluations and records the summary statistics shown. Sample size Sample mean Sample standard deviation Population standard deviation Standard deviation of ?¯ Confidence level ? ?⎯⎯⎯ ? ? ??⎯⎯⎯⎯ ? 38 4.0414 1.0501 0.9903 0.1606 90% The department chair determines the standard deviation of the sampling distribution of ?⎯⎯⎯ using
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 38 evaluations and records the summary statistics shown.
| Sample |
Sample standard deviation | Population standard deviation | Standard deviation of ?¯ | Confidence level | |
|---|---|---|---|---|---|
| ? | ?⎯⎯⎯ | ? | ? | ??⎯⎯⎯⎯ | ? |
| 38 | 4.0414 | 1.0501 | 0.9903 | 0.1606 | 90% |
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 90% confidence interval for ?, the mean overall rating students gave their Introductory Statistics lecturers. Round your answers to the nearest hundredth.
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