NAME:_________
You may use additional
sheets of paper to solve the following questions, but please report your
results and conclusions in the space provided.
Whenever possible, show your work for potential partial credit. NOTE:
When performing numerical calculations, keep at least 4 digits after a
decimal. (I.e., do NOT round .2265 to
.23 or .227) BUDGET YOUR TIME WISELY!
1. What important roles do the population mean (m) and standard deviation (s) play in the normal distribution? Using diagrams, show how different values of both
m and s will alter the curve.
(10 points)
2. The time, in minutes, for which a student
uses a computer terminal at the computer center of a major university, follows
an exponential probability distribution with a mean of 36 minutes. Assume a student arrives at the terminal just
as another student is beginning to work on the terminal.
a. What is the probability that the wait for the
second student will be 15 minutes or less?
(4 points)
b. What is the probability that the second
student will have to wait an hour or more?
(5 points)
3. Suppose I want to use a sample of college
students to make predictions on the overall dating habits (as measured by the
proportion who report in a survey that they are currently dating someone) for
the population of all college students in the U.S. In general, describe the sampling
distribution for the mean proportion of students in a relationship. Include the expected value and standard
deviation. Describe the important role
that the Central Limit Theorem plays here.
Use diagrams where necessary. (15
points)
4. According to USA Today (April 11,
1995), the mean number of days per year that business travelers are on the road
for business is 115. The standard
deviation is 60 days per year. Assume
that these results apply to the population of business travelers and that a
sample of 50 business travelers will be selected from the population.
a. What is the probability that the sample mean
will be more than 115 days per year? (5
points)
b. What is the probability that the sample mean
will be within 5 days of the population mean?
(6 points)
5. Your nosy roommate, reading over your
shoulder while you study, asks you to explain a 90% confidence interval and why
we find it useful to construct them.
Spend a little time explaining to her how confidence intervals relate to
population parameters, sampling distributions and sampling error. Be thorough, she has had no exposure to the
concepts. Feel free to use an example if
that helps her understand. (15 points)
6. A local newspaper reports that a random
sample of 16 U.S. college students rate their “quality of life” as an average
of 6.9848; where 10 is the highest. The
sample standard deviation is 1.9821.
Construct a 95% confidence interval estimate for the population mean
ranking of “quality of life”. Explain
what your interval tells you. If you
were the President of a college, would you be concerned? Why? (12 points)
7. Suppose that a national study of college alumni says that a good indicator of whether alumni donate money back to their alma mater is the proportion of alumni who would attend the college again, if given the chance. If this proportion is below .75, the college should be concerned about future donations and alumni support. You have surveyed 116 current Hanover College students and in response to the question: “Knowing what you know now, and if you were a senior in high school, would you choose Hanover again?” the sample proportion that said “yes” was .6897. Develop a hypothesis test to determine whether Hanover College should be concerned about future donations. Explain why you set it up the way that you did, choose an appropriate level of significance and clearly explain the results of your test and what it means to an administrator whose job it is to contact alumni for donations. (18 points)
8. What is a p-value and how is it used to
conduct a hypothesis test? Use the test
from #7 above as a good illustration.
(10 points)