Question

It has been found that candidates for an MBA program have undergraduate grade point averages that are normally distributed with standard deviation .45. A random sample of 25 applicants is taken, yielding a sample mean GPA of 2.90. (a) (10 points) Find a 95% confidence interval for the population mean GPA. (b) (5 points) Without doing the calculations, state whether a 90% confidence interval for the population mean would be wider or narrower than that in part (a). (c) (5 points) If we decide to calculate a 95% confidence interval based on a random sample of 20 applicants, would that interval be wider or narrower than the one found in part (a)? (d) (5 points) In fact, the population standard deviation is .15. State whether a correctly calculated 95% confidence interval would be wider or narrower than that in part (a).

          It has been found that candidates for
an MBA program have undergraduate grade point averages that are
normally distributed with standard deviation .45.  A random
sample of 25 applicants is taken, yielding a sample mean GPA of
2.90. 
           
(a) (10 points) Find a 95% confidence interval for the population
mean GPA.
           
(b) (5 points) Without doing the calculations, state whether a 90%
confidence interval for the population mean would be wider or
narrower than that in part (a).
           
(c) (5 points) If we decide to calculate a 95% confidence interval
based on a random sample of 20 applicants, would that interval be
wider or narrower than the one found in part (a)?
           
(d) (5 points) In fact, the population standard deviation is .15.
State whether a correctly calculated 95% confidence interval would
be wider or narrower than that in part (a).

Added by Michael G.

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