After numerous studies, it is estimated that the age of collegestudents follows a normal distribution with a mean of 20.7 yearsand a standard deviation of 1.8 years. A random sample of 16college students is taken and the sample mean and sample standarddeviation are found to be 21.5 years and 2.5 years,respectively.
a. Is the sample average of 21.5 considered an outlier (in otherwords, what is the chance of getting a sample mean at least aslarge as 21.5)?
b. The calculated value of the sample standard deviation islarger than σ, is 2.5 years enough larger than 1.8 that theestimate of σ does not seem reasonable?
c. No matter what you got for an answer in part b, assume we nolonger trust σ = 1.8 to be valid. Calculate the same probability asyou did in part a, but this time, assume that σ is unknown.
d. Is there a significant difference in parts A and C?
