A college admissions officer for an MBA program has determined that
historically applicants have undergraduate grade point averages that are
normally distributed with standard deviation 0.45. From a random sample
of 25 applications from the current year, the sample mean grade point
average is 2.90.
(a) Find a 95% condence interval for the population mean?

(b) Without doing calculations, explain whether a 99% condence interval
for the population mean would be wider than, narrower than, or the
same width as found in part (a).

(c) Suppose that population standard deviation is 0.56 (instead of 0.45),
without doing calculations explain whether a 95% condence interval
for the population mean would be wider than, narrower than, or the
same width as found in part (a).

(d) Suppose that sample mean that is given in the problem is calculated
from a sample of size 40 (instead of 25), without doing calculations
explain whether a 95% condence interval for the population mean
would be wider than, narrower than, or the same width as found in
part (a).

(e) Based on these sample results, a statistician computes for the popula-

tion mean a condence interval extending from 2.81 to 2.99.

Find the confidence level associated with this interval

(f) Suppose that we know that grade point averages that are normally dis-
tributed, but we don't have the population standard deviation. From
a random sample of 25 applications from the current year, the sample
mean grade point average is 2.90, and sample standard deviation is
found to be 0.40. Find a 95% condence interval for the population
mean?