STAT 100 - Midterm II Sample Exam (short) SOLUTIONS Spring 2013

STAT 100 - Midterm II
STAT 100 - Midterm II
Sample Exam (short)
SOLUTIONS
Spring 2013
Instructions
1.
2.
3.
4.
5.
6.
Do not panic. It rarely helps.
Read all questions carefully.
Write your answers clearly in the spaces provided.
Where computations are required, you should show work.
Cross out any material you do not wish to have considered.
Correct answers with insufficient justification or accompanied by additional incorrect
statements will not receive full credit.
7. Write all answers on the exam itself.
8. The exam has 33 total marks
Name: ____________________________________________
Student Number: ____________________________________________
Signature: ____________________________________________
Useful formula:
The counting rule for a median is
z=
r=
observation − mean
standard deviation
and
( n + 1)
2
percentile = mean + z × ( standard deviation )
n
⎛ x − x ⎞ ⎛ yi − y ⎞
1
⋅ ∑⎜ i
n − 1 i=1 ⎝ sx ⎟⎠ ⎜⎝ sy ⎟⎠
index number =
value
× 100
base value
dollars at time B = dollars at time A ×
CPI at time B
CPI at time A
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STAT 100 - Midterm II
QUESTION 1 (5 points)
A random sample of patients who attended a clinic was selected. The age of the patient (years)
and the number of days since the last visit were collected and are displayed in the figure below.
The least-squares regression line for predicting number of days since the last visit from the age
of the patient is y = 600.081 – 8.694x.
Days Since Last Visit
500
375
250
125
0
0
18
35
Age of Patient
53
70
A. The slope of this line is: (Ans: C)
A) 600.081.
B) 8.694.
C) –8.694.
D) 600.081 – 8.694 = 591.387.
B. The slope of this line tells us the (Ans: C)
correlation between age of patient and days since last visit.
b) change in days since last visit for each year older a patient is, on average.
c) change in the age of the patient for each extra day since the last visit.
d) average days since last visit for all of the patients.
a)
C. Using this line, you predict that the number of days since last visit to the clinic for a 50-yearold patient will be about: Ans: C
A) 63 days.
B) 78 days.
C) 165 days.
D) 200 days.
E) 252 days.
D. A least-squares regression line is not just any line drawn through the points of a scatterplot.
What is special about a least-squares regression line? (Ans: E)
a)
b)
c)
d)
e)
It passes through all the points.
It minimizes the squared values of the data.
It has slope equal to the correlation between the two variables.
It describes how a response variable y changes as an explanatory variable x takes different
values.
It minimizes the sum of the squared vertical distances of the data points from the line.
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STAT 100 - Midterm II
Question 2
Consider a large number of countries around the world. There is a positive correlation between
the number of Nintendo games per person x and the average life expectancy y. Does this mean
that we could increase the life expectancy in Rwanda by shipping Nintendo games to that
country? Explain.
Solutions
No. The positive correlation just shows that richer countries have both more Nintendo games per
person and higher life expectancies.
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STAT 100 - Midterm II
Question 3
Answer the questions below about the graph above, which shows a histogram with a normal
density that has the same mean and standard deviation as the data.
A. (1 pt) Which of the following is the mean of the data? (Choose one) (Ans: B)
a)
12.1%
b. 0.019
c. 0.005
d. 16.2%
B. (1 pt) Which of the following is the standard deviation of the data (Choose one) (Ans: C)
a)
0.055
b. 18.4%
c. 0.0125
d. 10.0%
C. (1 pt) In what interval is the first quartile of the data?
.0075 to .0125
- ½ mark if they just say .010.
D. (1 pt ) In what interval is the 90th percentile of the data?
.0325-.0375 - ½ mark if they just say .035
E. (2 pts) Is the normal density a good model for these data? Explain.
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STAT 100 - Midterm II
No. Data show a right-skew pattern (long tight tail, short left tail). Normal density is
symmetric. (Normal model expects more data at and below 0, and less data below the
mean, and in the far right tail.) Any words that clearly express this concept are fine.
Give partial credit for partially correct ideas. For example, saying only that the normal
density does not fit the data without any specifics is worth 1.5.
Question 4
A. (2 pts) Describe the relationship between X and Y.
1. Direction: Positive (increasing)
2. Shape: Fairly straight line (may note a slight wiggle if they want
3. Strength: Not very tight to line/not very strong
4. Deviations: Possible outliers between x=5-6
½-mark each for comments on direction, shape, strength, and deviations. Be accepting
of alternative interpretations that are believable
B. (1 pt) On the plot above, draw in your best guess for where the regression line would go.
Answers will vary. Look at plot: does it seem to go through the middle of the data? If so,
give full marks. If clearly biased but still sort of middle, give ½.
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STAT 100 - Midterm II
Question 5
A. (5 pts) A sample was taken of the salaries of 10 employees of a large company. The following
are the salaries (in thousands of dollars) for this year.
41
67
28
52
42
102
61
48
42
34
Calculate a 5-number summary for these data. Place your 5 numbers in the blanks below in
order from smallest to largest.
Question 6
The graphic at right was circulated
around Facebook shortly before the
2012 US Presidential Election. For
reference, US presidents are elected
every four years and take office in the
January after their election.
Comment on how accurately the
graphic represents the factual
statement that 4,400 jobs have been
lost in coal-related industries since
Obama took office.
Solutions
The “y” axis on the graphic does
not extend to zero, so the decrease
in jobs looks much more severe that it really is (it looks like almost ¾ were lost, but really
should depict about a 6000/88000 = 7% decline over the time period shown)
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STAT 100 - Midterm II
The time period does not extend all the way to the beginning of Obama’s taking office.
(In fact, since the plot shows a decline of 6000 from start to finish, that means that there
were about 1600 jobs gained from Jan 2009-Sept 2011!
1 mark for each item. 1 bonus mark for discovering the underlined statement.
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