STAT 100 Midterm 1
INSTRUCTIONS: Answer all questions on all pages. Write your answers clearly in the spaces
provided. Where computations are required, you should show work. Incorrect answers without
clearly-displayed work cannot be considered for partial credit. If a question calls for an
explanation, provide one that is complete. Do not omit important details or include irrelevant or
incorrect statements. True/False or multiple choice questions need not be accompanied by an
If you have difficulty, or feel like you are working slowly, solve the easiest problems first.
Total points on exam: 28
Short answers, explain – sentence or two
“So act that your principle of action might safely be made a law for the
-Immanuel Kant, philosopher (1724-1804) STAT 100 Midterm 1, Fall 2009
QUESTION 1 (6 pts)
3417 people were recently selected at random from all adult taxpayers in Canada and answered
questions about the Canada Revenue Agency (CRA) assessments.
A. (1 pt) What was the population for the study?
Adult taxpayers in Canada
B. One question was, “Do you feel that CRA assessments are accurate?” 2137 answered
a. (1 pt)Estimate the percentage of the population that feels that the CRA
assessments are accurate.
2137/3417 = 0.6254 = 62.5% (rounding to 63% is OK)
b. (1 pt) Find the margin of error for the estimate.
Margin of error 1/√3417=1/58.46 – 0.017 or 1.7% (rounging to 2% is OK)
c. (1 pt) Explain what the margin of error tells you about the population here.
We are 95% confident that the study estimates the percentage of adult taxpayers in Canada
who believe assessments are accurate withingg+/- 1.7%. Alternatively, we can say that 95%
confidence we believe that the percentage of adult taxpayers who feels that CRA assesments
are accurate is between 60.8% and 64.2% if given a generic interpretation without
mentioning detaisl and numebrs that is give half mark
Definition of margin or error
C. (2 pts) Suppose that three years ago another survey of about the same size asked the
same question and got an estimate that was statistically significantly lower than the
current estimate. Between that survey and this one, CRA began a new program to
improve their assessment accuracy. Can they claim that the new program has been
They cannot claim that the program is successful. The best reason is that the cause of the
increase may be some other factor unrelated to the new program (a “lurking variable”) (2marks)
2 STAT 100 Midterm 1, Fall 2009
A less goood answer: statistical significance may have been accidental and the program may not
have chagned anything, but unusual sampling variability resulted in very different results
QUESTION 2 (4 pts)
The table at right lists the number of grouse sigYear Age Gender Sightings
by a wildlife manager at a certain wildlife park 1993 I M 103
1993 I F 99
over 5 years. He would like to try to figure out 1993 F F 139
whether the different ages (Adult or Immature) and
1993 F M 85
genders (Female and Male) have any effect on the 1994 I M 145
1994 I F 168
number of sightings.
1994 F F 298
1994 F M 122
1995 I M 68
A. List any response variables: 1995 I F 93
1995 F F 205
1995 F M 87
1996 I M 105
1996 I F 148
1996 F F 171
B. List any explanatory variables: 1996 F M 69
1997 I M 147
1997 I F 169
1997 A F 175
1997 A M 95
1998 I M 110
C. Select any variable and list its values: 1998 I F 119
1998 A F 150
1998 A M 87
4 possible answers (see table)
year, or age, or gender, or sightings
QUESTION 3 (2 pts)
Below are some measurements and corresponding instruments for each one indicate whether it is
likely to be a valid measurement (in the blank, respond YES for valid or NO for not valid)
3 STAT 100 Midterm 1, Fall 2009
A. Using movie rating (G, PG, 14A, 18A, R) to measure the appropriateness of
a film for children
B. Using length of a movie as a measure of its quality
C. Using an x-ray as a measure of the presence of a fracture
D. Using a written driver’s test as a measure of driving ability
QUESTION 4 (6 pts)
A study was performed on the effects of distractions on studying. A room at a university
was set up with a sound system and a TV. Student volunteers who entered the room were
exposed to either (1) loud rock music, (2) soft baroque music, (3) an adventure movie on the
TV, or (4) quiet (no TV or music).
The student volunteers first took a brief pre-test. The students were placed into groups
according to scores on the pre-test: the top 4 formed the first group, the next 4 highest
formed the second group, and so on. There were 20 volunteers, so there were 5 groups.
From each group, one student was exposed to the loud rock, one to the soft baroque, one to
the TV, and one to the quiet. Every student was given some materials to read and study for
an hour. At the end of the hour, each student took a final test on the materials.
A. (1 pt) What kind of study is this?