Students in introductory statistics class were asked to report age of their mothers when they were born. Summary statistics include
Sample size: 36 students Sample mean: 29.643 years
Sample standard deviation: 4.264 years
a. Compute the standard error of this sample mean.
b. Find out and interpret a 90% confidence interval for mother's mean age (at student's birth) in the population of all students at this university.
c. How would 99% confidence interval compare to 90% interval in terms of its midpoint and half-width?
d. Would you expect 90% of the ages in the sample to be in the 90% confidence interval? Discuss why or why not.
e. Even if distribution of mothers' ages were somewhat skewed, would this confidence interval procedure still be valid with these data? Explain why or why not.