Download sample exam 2

STAT 100
Sample Mid-term Examination #2
The following questions are similar to the types of questions you will see on the midterm
exam. The actual midterm will be roughly 30 multiple-choice questions. No calculator
should be required.
Question 1. In a study of the relationship between handspan (in centemeters) and height
(in inches) it was found that the correlation is about .80 and the regression equation
is
handspan = −4 + 0.4 × height
What is the predicted handspan for someone 5 feet (60 inches) tall?
(A) 4 centimeters
(B) 20 centimeters
(C) 60 centimeters
(D) 48 centimeters
Question 2. True or False: The addition of outliers in a scatter plot can increase the
correlation.
(A) True
(B) False
Question 3. Consider the following two variables: Weight of a car and its gas mileage (the
number of miles it can drive on a gallon of gasoline). We would expect the correlation
to be
(A) positive
(B) zero
(C) negative
(D) one
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Use the following for the next three questions:
Here is a hypothetical research question, asked of a random sample of students: Do you
own a pet? (Data and related output below.)
Rows:
Female
Male
All
Gender
no
26
17
43
Columns:
yes
50
18
68
Pet
All
76
35
111
Chi-sq = 0.40 + 0.25 +
0.87 + xxxx = 2.08
The research hypothesis is that there is a relationship
between gender and whether or not the person owns a pet.
Question 4. In the debate between the research advocate and the skeptic, who wins in
this case involving the pet question?
(A) Both
(B) Research advocate
(C) Neither
(D) Skeptic
(E) Not enough information is given to answer this question.
Question 5. In the table, the expected number corresponding to 18 is given by:
(A) 182 /111
(B) (18 − 68)2 /68
(C) (43 × 76)/111
(D) (35 × 68)/111
(E) (18 − 68)2 /111
Question 6. If all the counts in the table were multipled by 10, the chi-squared value would
(A) change to 208
(B) stay the same
(C) change to 20.8
(D) change to .208
Question 7. Suppose that 1% of the population has hepatitis. Suppose we have a test for
the disease that has 80% sensitivity and 90% specificity. What is the probability of a
false positive?
(A) 0.01
(B) 0.20
(C) 0.99
(D) 0.10
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Question 8. The variables x (temperature in ◦ C) and y (temperature in ◦ F) are related
by the formula y = 32 + 1.8x. Therefore the correlation between x and y will be:
(A) 1, because the variables have a deterministic, linear, increasing relationship.
(B) 32, because if y = 32 then x = 0.
(C) 0, because if x = 0 then y = 32.
(D) 1.8, because if x increases by 1◦ C then y increases by 1.8◦ F.
(E) −1, because if x decreases then y decreases.
Question 9. Suppose that 1% of the population has hepatitis. Suppose we have
a test for the disease that has 80% sensitivity and 90% specificity. What is
P (hepatitis given that the test is positive)?
(A) (0.8 × 0.01)/(0.8 × 0.01 + 0.1 × 0.99)
(B) 0.01
(C) (0.2 × 0.01)/(0.2 × 0.01 + 0.9 × 0.99)
(D) 0.8
(E) (0.8 × 0.01)/(0.8 × 0.01 + 0.9 × 0.99)
Question 10. In an example in the textbook, the correlation between wives’ and husbands’
heights, in millimeters, was 0.36. If heights are measured in inches then the correlation
will:
(A) Decrease, because 1 millimeter is shorter than 1 inch.
(B) Be unchanged, because correlation does not depend on the units of measurement.
(C) Increase, because 1 inch is longer than 1 millimeter.
(D) Become zero; for there is no correlation between the two variables.
(E) None of the above.
Question 11. Suppose you are playing a game and you have 0.3 probability of winning.
Suppose you decide to play repeatedly until you win. The games are independent.
What is the probability that you win on the first or second try?
(A) 0.32
(B) 0.3 + 0.7 × 0.3
(C) 0.3 + 0.7
(D) 0.7 × 0.3
3
The following table presents experts’ and students’ rankings of the risks of eight activities. (Hint: Sketch the scatterplot of these rankings with the experts’ rankings on the
horizontal axis.)
Activity or Technology
Motor Vehicles
Smoking
Alcoholic Beverages
Handguns
Surgery
Motorcycles
X-rays
Pesticides
The Eight Greatest Risks
Experts’ Rank (x) Students’
1
2
3
4
5
6
7
8
Rank (y)
5
3
7
4
11
6
17
2
Question 12. If “Pesticides” were deleted from the data above then we would expect that:
(A) The correlation and the slope of the regression line both will increase.
(B) The correlation and the slope of the regression line both will remain unchanged.
(C) The correlation will increase and the slope will decrease.
(D) The correlation and the slope of the regression line both will decrease.
(E) None of the above.
Question 13. The technology “Nuclear Power” was ranked 1 by the students and 20 by
the experts. If “Nuclear Power” were to be added to the above list then we could
expect that:
(A) The correlation and the slope of the regression line both will increase.
(B) The correlation will increase and the slope will decrease.
(C) The correlation and the slope of the regression line both will remain unchanged.
(D) The correlation and the slope of the regression line both will decrease.
(E) None of the above.
4
−40
−35
Question 14. Consider the scatterplot below.
●
●
●
●
●
●
●
●
−45
●
●
●
●
●
−50
●
●
●
●
●
−55
y
●
●
●
●
●
● ●
●
●
●
●
●
●
● ●
●
●
●
●
●
● ●
●
−60
●
●
●●
−65
●
●
●
●
−70
●
80
90
100
110
120
x
One of the numbers below is the correct correlation of the variables in the scatterplot.
Which one is it?
(A) −.61
(B) 0
(C) 8
(D) −1
(E) .52
Question 15. The variables x (temperature in ◦ C) and y (temperature in ◦ F) are exactly
related by the formula y = 32 + 1.8x. Which of the following statements is true for a
sample of observed temperatures measured in both Fahrenheit and Celsius?
(A) The slope of the regression equation and the correlation coefficient have opposite signs.
(B) The slope of the regression equation and the correlation coefficient both equal 1.8.
(C) The slope of the regression equation is 1.8 and the correlation coefficient is 32.
(D) The slope of the regression equation is 1.8 and the correlation coefficient is 1.
Question 16. Consider the following two variables measured on a sample of people: Height
(in inches) and weight (in pounds). We would expect the correlation to be
(A) −1
(B) between −1 and 0
(C) 0
(D) between 0 and 1
(E) 1
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Question 17. The game “odd man” is played as follows: Three people all flip a coin. If
one of the players has a different outcome than the other two, that player is the loser.
Otherwise, the game is a draw. What is the probability that a game of odd man ends
in a draw?
(A)
(B)
(C)
(D)
(E)
1
1
8 + 8 , or 0.25
7
7
8 + 8 , or 1.75
1
8 , or 0.125
7
7
8 × 8 , or 0.766
1
2 , or 0.5
Question 18. Here is a hypothetical research question, asked of a random sample of students: Do you like broccoli? (Data are given below.)
Female
Male
All
Like broccoli?
no
yes
9
11
11
9
20
20
All
20
20
40
Calculate the chi-squared statistic for this example. What is the value of the chisquared statistic? (Hint: The math is possible to do by hand.)
(A)
(B)
(C)
(D)
(E)
4
10
2
10
5
10
1
10
3
10
= 0.4
= 0.2
= 0.5
= 0.1
= 0.3
Question 19. In a randomized experiment involving a new vitamin supplement intended
to reduce the chances of catching a cold, suppose that subjects were randomly divided
into two groups of 100 each. Over the course of an entire winter, 13 of the subjects
receiving the supplement got colds and 24 of those not receiving the supplement got
colds. In this study, what is the risk for the treatment group?
(A)
(B)
(C)
(D)
(E)
24
76
24
100
13
24
13
87
13
100
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Question 20. Suppose a door prize winner is selected at random from all the people
attending an Italian electrical engineering conference. Your roommate believes that
the winner is more likely to be a black-haired male than a male in general. Your
roommate has committed
(A) the anchoring fallacy.
(B) no fallacy at all; it is well-known that men with black hair have more fun.
(C) the gambler’s fallacy.
(D) the conjunction fallacy.
Question 21. In a study of the relationship between ideal weight and actual weight,
both measured in pounds, it is found that the correlation is 0.867 and the regression
equation is
Idealwt = 25.6 + 0.779 × Actualwt.
What is the expected increase in the response variable for every increase of one in the
explanatory variable?
(A) 25.6 pounds
(B) 0.779 pounds
(C) 0.867 pounds
(D)
(E)
1
.867 , or 1.153 pounds
1
.779 , or 1.284 pounds
Question 22. Suppose you hear a salesman on a television commercial say, “Would you
pay sixty dollars for this product? We’re now selling it for only $19.99!” Which of
the following is the salesman exploiting?
(A) The law of large numbers
(B) Confusion of the inverse
(C) Anchoring
(D) The conjunction fallacy
(E) The law of small numbers
Question 23. Suppose you have to cross a train track on your commute. The probability
that you will have to wait for a train is 1/5, or .20. If you don’t have to wait, the
commute takes 15 minutes, but if you have to wait, the commute takes 20 minutes.
What is the expected value of the time it takes you to commute?
(A) (20 + 15) × 51 , or 7 minutes
(B) 20 × 51 , or 4 minutes
(C) 20 ×
(D)
(E)
1
5
15+20
2 ,
20 × 15
+ 15 × 45 , or 16 minutes
or 17.5 minutes
+ 15, or 19 minutes
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No Ticket Ticket Total
Female
52
25
77
Question 24. Male
17
19
36
Total
69
44
113
The data show clearly that males received traffic tickets at a higher rate than females. From
these census data we conclude that the events “Female” and “Ticket” are:
(A) Both mutually exclusive and independent
(B) Mutually exclusive
(C) Neither mutually exclusive nor independent
(D) Independent
Question 25. A certain test for hepatitis has a sensitivity of 90%. What does this mean?
(A) 90% of individuals who have hepatitis will test positive.
(B) 90% of individuals who have hepatitis will test negative.
(C) 90% of individuals who do not have hepatitis will test negative.
(D) 90% of individuals who do not have hepatitis will test positive.
Question 26. A fair die if rolled repeatedly until the first six appears. What is the
probability that the first six appears on the fourth roll?
(A) ( 56 )6
(B)
4
6
1
5
6 × 6
5
5
5
6 × 6 × 6
(C) 3 ×
(D)
×
1
6
Question 27. Suppose you flip a fair coin until the first occurrence of heads. What is the
probability that the first occurrence of heads occurs on the third flip?
(A) 1 −
1
2
×
1
2
, or .75
(B) 12 , or .5
(C)
(D)
1
2
1
2
×
+
1
2
1
2
× 21 , or .125
+ 12 , or 1.5
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Question 28. A random sample of students was asked the following question: “Are your
parents divorced or separated?” The data are given below.
Female
Male
All
Div/sep?
No Yes
99
34
77
24
176
58
All
133
101
234
What is the expected count (assuming the skeptic is correct) corresponding to the 99
in the upper left?
(A)
(B)
(C)
77×34
234 , or 11.19
99
133 , or .74
99
234 , or .42
(D) 99
(E)
176×133
234 ,
or 100.03
Question 29. The probability of winning a game of craps is equal to .493. You decide
you are going to play craps repeatedly until you win a game. What is the probability
that your first win occurs on the second game of craps?
(A) .507
(B) .493 + .507
(C) .507 × .493
(D) .493
(E) .4932
Question 30. Suppose that in a particular sample, we find that 80% of female college
students use cell phones while 75% of male college students use cell phones. Which
of the following is true?
(A) This difference between males and females is less likely to be statistically significant if
the sample is larger.
(B) This difference between males and females is less likely to be practically significant if
the sample is larger.
(C) This difference between males and females is more likely to be practically significant if
the sample is larger.
(D) This difference between males and females is more likely to be statistically significant
if the sample is larger.
9
Question 31. Suppose the probability that a child lives with his or her mother as the sole
parent is .216, and the probability that a child lives with his or her father as sole
parent is .031. Then the probability that a child either lives with both or with neither
parent is:
(A) 1 − .031 = .969
(B) 1 − (.216 + .031) = .753
(C) .216 + .031 = .247
(D) 1 − .216 = .784
(E) None of the above
Question 32. A dataset contains yearly measurements since 1960 of the divorce rate (per
100,000 population) in the United States and the yearly number of people (per 100,000
population) sent to prison for drug offenses in the United States. We observe a strong
correlation of .67. Each of the following statements is true EXCEPT
(A) A positive correlation exists between divorce rates and drug lockups.
(B) Higher divorce rates lead to higher rates of drug lockups.
(C) Years with higher divorce rates have tended to be years with higher lockup rates.
(D) Higher divorce rates are associated with higher rates of drug lockups.
Question 33. Suppose that a particular over-the-counter pregnancy test has a sensitivity
of 90% and a specificity of 99%. What is the false positive probability?
(A) 5%
(B) 10%
(C) 90%
(D) 1%
(E) 99%
Question 34. Suppose you repeatedly toss a coin for which the probability of tossing heads
is .3, or 30%. The probability that you do not toss heads on any of your first four
tosses is:
(A) .7 + .7 + .7 + .7 = 2.8
(B) (.7)4 = .24
(C) 1 − (.7)4 = .76
(D) .7
(E) None of the above
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