Decision Sciences
Sergio Koreisha
Confidence Interval Problems
2. A process producing bricks is known to give an output whose weights are normally
distributed with standard deviation .12 pound. A random sample of sixteen bricks from
today's output had mean weight 4.07 pounds.
(a) Find a 99% confidence interval for the mean weight of all bricks produced this day.
(b) Without doing the calculations. state whether a 95% confidence interval for the population
mean would be wider than, narrower than, or the same width as that found in (a).
(c) It is decided that tomorrow a sample of twenty bricks will be taken. Without doing the
calculations, state whether a correctly calculated 99% confidence interval for the mean weight
of tomorrow's output would be wider than, narrower than, or the same width as that found in
(a).
(d) In fact, the population standard deviation for today's output is .15 pound. Without doing
the calculations. state whether a correctly calculated 99% confidence interval for the mean
weight of today's output would be wider than narrower than, or the same width as that found
in (a).
4. A college admissions officer for an M.B.A. 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% confidence interval for the population mean.
(b) Based on these sample results, a statistician computes for the population mean a
confidence interval extending from 2.81 to 2.99. Find the confidence level associated with
this interval.
5. Koca Kola wants to estimate the mean income of its blue-collar market segment. It selects
8 families from the segment and obtains the following income data. Assume the population
distribution is normal.
26,700 32,400
31,000 30,675
21,500 20,550
28,500 25,500
a. Construct 99% confidence interval on the mean income.
b. The marketing manager believes that the population mean income for the blue-collar
segment is above $21,500. Is the manager correct in her assessment? Explain.
