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Quiz: Midterm Test
Midterm Test
Started: Mar 20 at 3:15pm
Quiz Instructions
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Question 1 1 pts
The independent variable of interest in an ANOVA procedure is called a
partition.
factor.
response.
treatment.
An experimental design where the experimental units are randomly assigned to the treatments is known as _____ design.

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Question 2 1 pts
factor block
random factor
completely randomized
randomized treatment
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Question 3 1 pts
The cumulative probability distribution shows the probability:
of all possible events occurring.
that a random variable is less than or equal to a particular value.
that a random variable takes on a particular value given that another event has happened.
of two or more events occurring at once.
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Question 4 1 pts
The expected value of a discrete random variable:
is the outcome that is most likely to occur.
is computed as a weighted average of the possible outcome of that random variable, where the weights are the
probabilities of that outcome.
equals the population median.
can be found by determining the 50% value in the c.d.f.
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Question 5 1 pts
Let Y be a random variable. Then var(Y) equals:
.
E
.

E
E
.
.
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Question 6 1 pts
For a normal distribution, the skewness and kurtosis measures are as follows:
0 and 3
1.96 and 4
0 and 0
1 and 2
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Question 7 1 pts
The conditional expectation of Y given X, E(Y
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, is calculated as follows:
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Pr(X = xi)
E
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Question 8 1 pts
Two random variables X and Y are independently distributed if all of the following conditions hold, with
the exception of:
E(Y) = E[E(Y )].
knowing the value of one of the variables provides no information about the other.
Pr(Y = y

if the conditional distribution of Y given X equals the marginal distribution of Y.
= x) = Pr(Y = y).
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Question 9 1 pts
The correlation between X and Y:
is given by corr(X, Y) =
.
is the covariance squared.
can be calculated by dividing the covariance between X and Y by the product of the two standard deviations.
cannot be negative since variances are always positive.
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Question 10 1 pts
Two variables are uncorrelated in all of the cases below, with the exception of:
being independent.
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having a zero covariance.
E(Y
) = 0.
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Question 11 1 pts
Assume that Y is normally distributed N(μ, σ2). Moving from the mean (μ) 1.96 standard deviations to the
left and 1.96 standard deviations to the right, then the area under the normal p.d.f. is:
0.95
0.67
0.05
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Question 12 1 pts

0.33
The Student t distribution is:
always well approximated by the standard normal distribution.
the distribution of a random variable with a chi-squared distribution with m degrees of freedom, divided by m.
the distribution of the ratio of a standard normal random variable, divided by the square root of an independently
distributed chi-squared random variable with m degrees of freedom divided by m.
the distribution of the sum of m squared independent standard normal random variables.
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Question 13 1 pts
When there are ∞ degrees of freedom, the t∞ distribution:


has a bell shape similar to that of the normal distribution, but with "fatter" tails.
equals the standard normal distribution.
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can no longer be calculated.
equals the
distribution.
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Question 14 1 pts
The sample average is a random variable and:

has a probability distribution that is the same as for the Y1,..., Yn i.i.d. variables. 
is a single number and as a result cannot have a distribution.
has a probability distribution called the standard normal distribution.
has a probability distribution called its sampling distribution.
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Question 15 1 pts
Consistency for the sample average
can be defined as follows, with the exception of:


μY . 

the probability of
being in the range μY ± c becomes arbitrarily close to one as n increases for any constant c > 0. 
has the smallest variance of all estimators.

converges in probability to μY. 
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Question 16 1 pts
The mean and variance of a Bernoulli random variable are given as:
np and np(1-p)
p and (1- p)
cannot be calculated
p and
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Question 17 1 pts
Consider the following linear transformation of a random variable y =
where μx is the mean of x and
σx is the standard deviation. Then the expected value and the standard deviation of Y are given as:
0 and 1
1 and 1
Cannot be computed because Y is not a linear function of X
and σx
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Question 18 1 pts
Let Y be the total number (outcomes) of rolling a pair of dice, where Pr(Y=2)=Pr(Y=12)=1/36, etc. The
following statements are true, EXCEPT:
= 5.83

Pr(Y≤ 7)= 0.5
E(Y) = 7
skewness = 0
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Question 19 1 pts
Bayes' Rule states:
Pr( Y = y ∣ X = x) =
Pr( Y = y ∣ X = x) =
Pr( Y = y ∣ X = x) = Pr( X = x ∣ Y = y)
Pr( Y = y ∣ X = x) =
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Question 20 1 pts
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Quiz: Midterm Test
In a completely randomized design involving four treatments, the following information is provided.
Treatment 1
Treatment 2
Treatment 3
Treatment 4
Sample Size
55
18
15
20
Sample Mean
35
38
42
50
The overall mean (the grand mean) for all treatments is
39.25.
40.76.
40.0.
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Question 21 1 pts

41.25.
An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 25 observations,
were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value
of F are
4 and 124.
5 and 25.
4 and 120.
4 and 25.
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Question 22 1 pts
The critical F value with 8 numerator and 29 denominator degrees of freedom at α = 0.05 is
3.64.
3.33.
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2.28.
3.20.
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Question 23 1 pts
Consider the following information.
SSTR = 6,750
H0: μ1 =μ2 =μ3 =μ4 = μ5
SSE = 8,000
Ha: At least one mean is different
The mean square due to treatments (MSTR) equals
1,350.
500.

400.
1,687.5.
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Question 24 1 pts
Consider the following information with n = 5.
SSTR = 6,750
H0: μ1 = μ2 = μ3 = μ4 = μ5
SSE = 8,000
Ha: At least one mean is different
The null hypothesis is to be tested at the 5% level of significance. The p–value is
greater than 0.10.
between 0.025 and 0.05.
less than 0.01.
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between 0.01 and 0.025.
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Question 25 1 pts
Consider the following ANOVA table.
Source
Sum
Degrees
Mean
of Variation
of Squares
of Freedom
Square
Between Treatments
2,073.6
4
Between Blocks
6,000
5
1,200
Error
20
288
Total
29
F

The null hypothesis for this ANOVA problem is
μ1 = μ2 = μ3 = μ4.
μ1 = μ2 = ... = μ20.
μ1 = μ2 = μ3 = μ4 = μ5.
μ1 = μ2 = μ3 = μ4 = μ5 = μ6.
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Question 26 1 pts
Consider the following ANOVA table.
Source
Sum
Degrees
Mean
of Variation
of Squares
of Freedom
Square
Between Treatments
2,073.6
4
6,000
5
Between Blocks
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F
1,200
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Error
20
Total
29
288
The mean square due to treatments equals
518.4.
1,200.
8,294.4.
288.
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Question 27 1 pts
Assume that the relationship between test scores and the student-teacher ratio can be modeled as a

linear function with an intercept of 698.9 and a slope of (-2.28). A decrease in the student-teacher ratio
by 2 will:
reduce test scores by 2.56 on average
result in a test score of 698.9
reduce test scores by 2.28 on average
reduce test scores by 4.56 for every school district
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Question 28 1 pts
Consider the following ANOVA table.
Source
Sum
Degrees
Mean
of Variation
of Squares
of Freedom
Square
Between Treatments
2,073.6
4
6,000
5
Between Blocks
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F
1,200
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Error
20
Total
29
288
The null hypothesis is to be tested at the 1% level of significance. The null hypothesis should
not be rejected.
be revised.
not be tested.
be rejected.
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Question 29 1 pts
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly

assigned to the 3 treatments. You are given the results below.
Treatment
Observations
A
20
30
25
33
B
22
26
20
28
C
40
30
28
22
The null hypothesis for this ANOVA problem is
μ1 = μ2 = ... = μ12.
μ1 = μ2.
μ 1 = μ 2 = μ 3.
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μ1 = μ2 = μ3 = μ4.
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Question 30 1 pts
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly
assigned to the 3 treatments. You are given the results below.
Treatment
Observations
A
20
30
25
33
B
22
26
20
28
C
40
30
28
22
The mean square due to error (MSE) equals

34.
5.86.
36.
1.872.
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Question 31 1 pts
In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five
treatments (a total of 65 observations). Also, the design provided the following information.
SSTR = 300 (Sum of Squares Due to Treatments)
SST = 800 (Total Sum of Squares)
The sum of squares due to error (SSE) is
500.
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300.
1,600.
1,100.
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Question 32 1 pts
In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five
treatments (a total of 65 observations). Also, the design provided the following information.
SSTR = 300 (Sum of Squares Due to Treatments)
SST = 800 (Total Sum of Squares)
The number of degrees of freedom corresponding to between-treatments is
59.

60.
4.
5.
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Question 33 1 pts
An important application of the chi-square distribution is
testing for goodness of fit.
testing for the independence of two categorical variables.
All of these alternatives are correct.
making inferences about a single population variance.
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Question 34 1 pts
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Consider the following regression line:
= 698.9 – 2.28 × STR. You are told that the t-statistic on the
slope coefficient is 4.38. What is the standard error of the slope coefficient?
4.38
-1.96
0.52
1.96
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Question 35 1 pts
Consider the estimated equation from your textbook
= 698.9 - 2.28 STR, R2 = 0.051, SER = 18.6
(10.4)(0.52)
4.38.

The t-statistic for the slope is approximately:
67.20.
0.52.
1.76.
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Question 36 1 pts
In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five
treatments (a total of 65 observations). Also, the design provided the following information.
SSTR = 300 (Sum of Squares Due to Treatments)
SST = 800 (Total Sum of Squares)
The mean square due to treatments (MSTR) is
10.
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12.
75.
60.
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Question 37 1 pts
Part of an ANOVA table is shown below.
Source of
Sum of
Degrees
Mean
Variation
Squares
of Freedom
Square
Between Treatments
64
Within Treatments (Error)
8
2
100

Total
F
The number of degrees of freedom corresponding to between-treatments is
18.
2.
3.
4.
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Question 38 1 pts
If you had a two regressor regression model, then omitting one variable which is relevant:
will have no effect on the coefficient of the included variable if the correlation between the excluded and the included
variable is negative.
makes the sum of the product between the included variable and the residuals different from 0.
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can result in a negative value for the coefficient of the included variable, even though the coefficient will have a
significant positive effect on Y if the omitted variable were included.
will always bias the coefficient of the included variable upwards.
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Question 39 1 pts
In multiple regression, the R2 increases whenever a regressor is:
added unless there is heteroskedasticity.
added.
added unless the coefficient on the added regressor is exactly zero.
greater than 1.96 in absolute value.
β0 + β1x1 + + β2x2 , the interpretation of β1 is:

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Question 40 1 pts
In the linear multiple regression model with two independent variables, where E(Yi ∣ X1i = x1, X2i = x2) =
is the predicted difference in Y between two observations for a change of X1i by β1, controlling for X2i.
is the predicted difference in Y between two observations with a unit difference in X2 holding X1 constant.
the same as in the simple regression model when X1i was the only regressor.
is the predicted difference in Y between two observations with a unit difference in X1, holding X2 constant.
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Question 41 1 pts
A control variable:
indicates that it is under the control of the econometrician
has a coefficient that always has a causal interpretation, even if it is not of primary interest
is a regressor to hold constant factors that, if included, could lead the estimated causal effect of interest to suffer from
omitted variable bias
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should be excluded from the multiple regression since its coefficient is not a parameter of reduce heteroskedasticity in
the error term
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Question 42 1 pts
Part of an ANOVA table is shown below.
Source of
Sum of
Degrees
Mean
Variation
Squares
of Freedom
Square
Between Treatments
64
Within Treatments (Error)
Total
F
8
2
100
36.

The mean square due to treatments (MSTR) is
16.
15.
64.
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Question 43 1 pts
The process of using the same or similar experimental units for all treatments is called
replicating.
partitioning.
factoring.
blocking.
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Question 44 1 pts
A completely randomized design is useful when the experimental units are
heterogeneous.
homogeneous.
​clustered.
stratified.
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Question 45 1 pts
A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population
is known as a _____ test.
comparison
probability

goodness of fit
normality
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Question 46 1 pts
Provide an appropriate response.
A researcher wants to know if the time spent in prison for a particular type of crime was the same for
men and women. A random sample of men and women were each asked to give the length of sentence
received. The data, in years, are listed below. Use the Wilcoxon rank sum test to find W, the sum of the
ranks for the smaller sample, to test the claim that there is no difference in the sentence received by
each gender.
135.5
155.5
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115.5
173.5
125.5
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Question 47 1 pts
Provide an appropriate response.
A local school district is concerned about the number of school days missed by its teachers due to
illness. A random sample of 10 teachers is selected. The numbers of days absent in one year is listed
below. An incentive program is offered in an attempt to decrease the number of days absent. The
number of days absent in one year after the incentive program is listed below. Use the Wilcoxon signedrank test to find the test statistic ws to test the claim that the incentive program cuts down on the number
of days missed by teachers. Use α = 0.05. The difference is defined as the After Incentive-Before

Incentive.
-3.16
7
-2
1
2
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Question 48 1 pts
Provide an appropriate response.
A weight-lifting coach claims that a weight-lifter can increase strength by taking vitamin E. To test the
theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The
results are listed below. Thirty days later, after regular training supplemented by vitamin E, they are
tested again. The new results are listed below. Use the Wilcoxon signed-rank test to find the critical
value to test the claim that the vitamin E supplement is effective in increasing the athletes' strength. Use
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The difference is defined as the Before-After.
4.5
5
2
6
31.5
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Question 49 1 pts
You want to test whether the following sample of 30 observations follows a normal distribution. The mean of the sample
2
3
5
5
7
8
8
9
9
10
11
11
12
12
12
12
13
13
13
14
15
15
15
16
16
17
17
18
18
19

equals 11.83 and the standard deviation equals 4.53.
The p-value is
less than 0.005.
greater than 0.1.
between 0.05 and 0.1.
between 0.025 and 0.05.
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Question 50 1 pts
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Quiz: Midterm Test
The test statistic for goodness of fit has a chi-square distribution with k – 1 degrees of freedom provided that the expected
frequencies for all categories are
5 or more.
k or more.
2k.
10 or more.
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
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