You may use the extra 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. 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 32 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 12 minutes or less?
(3 points)
b. What is the probability that the wait for the
second student will be between 18 and 30 minutes? (4 points)
c. Your nosy roommate wants you to calculate the
probability that the second student waits exactly 32 minutes. What do you say to this person? Explain your reasoning. (6 points)
2. Assume the
a. What is the probability that a randomly
selected student will have a GPA of lower than 2.50? (3 points)
b. At what GPA would a student need to earn such
that he/she would have a GPA above 15% of the student body? (5 points)
c. Any student who graduates with a GPA of 3.90
or better, earns the distinction of graduating summa cum laude.[1]
What is the probability that a student will earn such an honor? (4 points)
3. Suppose I want to use a sample of college
students to make predictions on overall exercise habits (as measured by hours
of exercise per week) for the population of all college students in the
4. A sample of 142 students is taken from a
population of 975. The sample mean hours
of weekly exercise is 6.1373 hours with a sample standard deviation of 4.6258
hours.
a. Should we consider this population to be
finite or infinite? Explain. (3 points)
b. In this situation, what are the population
parameters and what are their values? (2 points)
c. In this situation, what are the point
estimators and what are their values? (2 points)
d. If another sample of 142 students were taken
from the same population, what is the probability of a sampling error of 1 hour
or less? (4 points)
5. You are reading an article that describes a
survey of recent college graduates. The
article says that students that major in economics earn an average of $41,500
in starting salary and benefits with a margin of error of $800. In the footnote of the article you see that
the researchers used a 90% level of confidence and that 119 people were
surveyed.
a. Use the above information to compute the
standard deviation of the sample of recent graduate starting salaries. (2
points)
b. Explain to a “person on the street” what the
above margin of error means. Why is it
necessary and/or useful? (6 points)
6. A national magazine reports that a random
sample of 142 U.S. college students rate their “quality of life” as an average
of 6.8225; where 10 is the highest. The
sample standard deviation is 1.7149.
Construct a 99% 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? (10 points)
7. The monthly cost of a two-bedroom apartment
in a particular city is reported to average $550. We want to test whether this average has
changed in recent years.
a. State the null and alternative hypotheses and
the level (α) at which you are conducting the test. Why did you set up the test in this way? (4
points)
b. What is your critical value(s) and where is
the rejection range(s)? Show in a
diagram. (2 points)
c. A sample of 36 apartments is selected. The sample mean rent is $562 per month with a
sample standard deviation of $40. Calculate
your test statistic. (2 points)
d. Clearly state your conclusion to the test and
explain what it means for the rental market in this city. (4 points)
8. Environmental health indicators include air
quality, water quality, and food quality.
Twenty-five years ago, 47% of
a. State the null and alternative hypotheses for
the test. (2 points)
b. Discuss both type I and type II errors for
the above hypothesis test. For each type
of error, what might be the ramifications for public health? (6 points)
c. Given your consideration of type I and type
II error, specify the level (α) at which you are conducting the test. Justify this decision. (3 points)
d. What is your critical value(s) and where is
the rejection range(s)? Show in a
diagram. (2 points)
e. Given the sample information provided to
you, calculate your test statistic. (2 points)
f. Clearly state your conclusion to the test and
explain what it means for environmental quality and public health. (4 points)