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 samp. of 38 evaluations and records the summary statistics shown. Sample Sample Sample standard Population standard Standard Confidence size mean deviation deviation error level 38 4.0414 1.0501 0.9903 0.1606 90% The department chair determines the standard error using ơ, the standard deviation calculated from all student evaluations submitted to her department. Assume the Stațtistics lecturers' ratings have the same standard deviation. Use this information to find the margin of error and the lower and upper bounds of a 90% confidence interval for u, the mean overall rating students gave their Introductory Statistics lecturers. Round your answers to the nearest hundredth.

4. A survey of 499 women for the American Orthopedic Foot and Ankle Society revealed that 38% wear flats to work. a. Find 99% confidence interval for the population proportion of women who wear flats to work.

The ages of undergraduate students at two universities (one in the east and one in the west) are being compared.  Researchers want to know if there is a difference in the mean age of students at the two universities.  The population standard deviations are known. The following data shows the results of samples collected at each institution:              School Location       n (sample size)        sample mean ( )         population standard deviation              West                      33                           25.78                       6.29              East                       35                           23.16                       7.52   What is the value of the test statistic for the previous problem?  (Enter your answer as a positive value even if you calculated a negative test statistic value i.e. if you calculated -1.311 you should enter 1.311).  Round your answer to 3 decimal places.