Question Details

PENI{
FOSTER
COLLEGE
INSTRUCTOR USE ONLY
GHADE GHADED BY
Date:
EXAMINATION NO,
050274
Name:
Introduction to Business Statistics
Proctored Final Examination
Instructions: All of the questions on this examination should be answered on the
sheets provided, Write your name and your student number at the top of each
sheet. Be certain to indicate the proper number before each of your answers.
Remember tq show your work if an answer requires a mathematical solution. If
you need additional space, you may write on the back of the answer sheets'
Answer any two of the fotlowing four questions, Each answer is worth 2Ao/o.
1. Assume you have a data set from a normally distributed random variable' Answer the
following questions about it.
a. Will the random variable be discrete, continuous, or neither? l-{ow'do you know?
b. will the data be qualitative or quantitative? How do you know?
2, Assume the following data were gathered by a manufacturer of a robotics component,
in unlts of days of continuous use until the component fails. There are 50 measurements
in this data set. Show a histogram of this data set with 10 bins of equal size,
spanning the range from the data minimum to the data maximum.
14t 139
L29 139
128 L24
139 128
L23 145
L42
135
143
133
t42
150
L47
135
130
136
136
136
127
130
160
133
148
135
161
t47
127
151
136
133
145
118
L27
131
t2L
134
137
154
145
133
131
L22
133
t44
119
125
723
136
1s5
122
120
139
131
L44
t2!
140
(Continued on reverse side)
Pr1941,(1204)
fi r'oc;{:srarei Finil! Exar.nination
3. A university has been tracking the percentage of alumni giving to its annual fund each
year for the past 10 years. The data is given here'
14o/o 13o/o !5o/o 21o/o L9o/o 24o/o 25o/o 2go/o 25o/o 31o/o
Answer the following questions about this data'
a. What are its mean and median?
b. What is the procedure for using mean and median to determine whether the data
is skewed, and if so, in what direction?
c. Apply the procedure you described to the mean and median computed in part a'
4. A nurse is considering going back to graduate school to earn a Ph'D. in biochemistry'
One of the schools she visits tells her that the average time to earn the degree she's
considering is 5.5 years. Show that this statement is not sufficiently precise by giving
two different explanations of what it might mean'
Answer any two of the following three questions. Each answer is wotth t5o/o.
5. In the diagram below, events A, B, and C are shown with numbers in various regions
of the graph indicating how many sample points lie in each. For example, the number 3
in the top left of the diagram indicates that there are 3 sample points in B that are not 'i';F'i!'
also in either A or C. ' .= r :'' '
a.
b"
Are the events A
Are the events A
and B independent?
o 8c and C n Bc mutuallY exclusive?
Proetored Final Exarnination
6, Under which of the following conditions would it be appropriate to use a Binomial
random variable? In each case, explain why your answer is correct'
a. A department will interview 10 candidates for a position, and call back for second
interviews those who answer the interview questions to the satisfaction of all the
interviewers. They hope to call back at least 3, but past experience suggests an
average of about 1 call back per 4 interviews'
b. A factory posts on the wall the number of days since its last safety infraction or
injury. In the past year, the factory has had a safety infraction or injury on 6 different
days. The factory is interested in the number of days that can be expected to
elaPse without an injury.
c. Fifteen of a doctor's patients have the same ailment. Studies have shown that
about 86,50lo of patients with this ailment respond to a certain drug. The doctor
prescribes the diug to all 15, but the number who will respond in this case is, of
course, not known in advance.
7. The mean time for a racecar driver's crew to perform a pit stop is 13'2 seconds, with a
standard deviation of 0.9 seconds. To maintain his current lead, the driver needs a pit
stop in 12.5 seconds or less. Assuming this random variable is normally distributed,
what is the probability of the driver getting the pit stop in a short enough time to
maintain his lead?
Answer any two of the following three questions. Each answer is wofth L5o/o.
8. From a sample of size 175, the sample mean is f = 54.37 and sample standard
deviation is s = 7.O7.
a. Construct a 95o/o confidence interval for the population mean and show your work'
b. Explain how your work in part a would have been different if the sample size had
been onlY 12 instead
g. A random sample from the population of registered voters in California is to be taken
and then surveyed about an upcoming election. What sample size should be used to
guarantee a sampling error of 3o/o or less when estimating p at the 95olo confidence
level?
1O. a. Explain the two conditions required for a valid Iarge-sample test of hypothesis for a
mean.
b. Explain the two different possible outcomes of a test of hypothesis'
Froctored FInatr Examinati*n