ECO 578 Part A Multiple Choice (1–16)
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v Part A: Multiple Choice (1–16)
Using the following
information to answer questions 1-8:
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2
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1
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3
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0
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1
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2
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0
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5
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1
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4
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_____1.
What is the mean?
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a)
1.90
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b)
2.11
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c)
1.73
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d)
1.66
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_____2.
What is the median?
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a)
1.00
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b)
1.50
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c)
1.60
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d)
1.90
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_____3.
What is the mode?
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a)
0
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b)
1
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c)
2
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d)
3
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_____4.
What is the range?
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a)
1
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b)
4
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c)
5
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d)
3
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_____5.
What is the variance?
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a)
1.66
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b)
2.77
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c)
1.76
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d)
3.11
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_____6.
What is the standard deviation?
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a)
1.66
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b)
2.77
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c)
1.76
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d)
3.11
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_____7.
What is the 1st quartile?
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a)
0
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b)
1
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c)
2
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d)
3
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_____8.
What is the 70th percentile?
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a)
1
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b)
1.5
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c)
2
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d)
2.5
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Questions 9-16 refer to the following frequency
distribution:
The following information represents the number of tons of
grain stored at the 60 grain elevators of central Soya, Inc.
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Class
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Frequency
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_____9.
What is the relative frequency for the class 170-174?
_____10.
What is the mean?
_____11.
What is the median?
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||||||||||||
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160-164
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6
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165-169
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14
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170-174
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16
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175-179
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13
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180-184
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11
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Total
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60
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_____12. What
is the mode?
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a)
16
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b)
170
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c)
172
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d)
174
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_____13. What
is the variance?
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a)
39.68
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b)
12.33
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c)
151.55
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d)
149.02
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_____14. What
is the standard deviation?
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a)
6.30
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b)
3.51
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c)
12.31
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d)
12.21
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_____15. What
is the 1st quartile?
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a)
168.21
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b)
167.07
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c)
167.57
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d)
167.71
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_____16. What
is the 70th percentile?
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a)
176.35
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b)
176.85
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c)
176.81
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d)
177.31
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v Part
B: True or False (17-30)
_____17. The
random sample is the most important, because statistical theory applies to it
alone.
_____18. In a frequency
distribution, the class mark is the number of observations that fall within
that class.
_____19. Original
class interval frequencies can be obtained by multiplying the respective
relative frequencies by the total number of observations.
_____20. The
sum of the class frequencies is equal to the number of observations made.
_____21. A
relative frequency distribution describes the proportion of data values that
fall within each category.
_____22. There
would be no need for statistical theory if census, rather than a sample was
always used to obtain information about populations.
_____23. The
arithmetic mean is the sum of the data values divided by the number of
observations.
_____24.
is
_____25. The
median always exists in a set of numerical data.
_____26.
means that A and B
are mutually exclusive events.
_____27. Mutually
exclusive events imply that if one event occurs, the other cannot occur. An
event (e.g.,
) and its complement are always mutually exclusive.
_____28.
_____29. Events
are independent when the occurrence of one event has no effect on the probability
that another will occur.
_____30. The
P(x) is always 0 ≤ P(x) ≤ 1.
v Part
C: Answer the following questions (31-39)
31. Name 3 types of
statistical samples
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1
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2
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3
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32. Name reasons why we use
samples instead of an entire population
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33. Name types of random
samples.
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34. Name the measure of central tendency.
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35. Name measures of spread
or variability.
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36. Show that you
understand the difference between a sampling error and a sampling bias.
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37. Name 4 parts of the
regression.
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38. When do we use the
regression?
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39. Explain the concept of
error and uncertainty as it relates to decision making.
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v
Part
D: Must show all your work step by step in order to receive the full credit; Excel
is not allowed. (40-50)
40. Train
A and Train B are two transportations that people can use to transport from
Boston to New York. Sample of times recorded in minutes for each train are
shown below.
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Train A
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28
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29
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32
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37
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33
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25
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29
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32
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41
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34
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Train B
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29
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31
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33
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32
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34
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30
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31
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32
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35
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33
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Please
answer the following questions (a-i).
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Train
A
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Train
B
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a)
Mean
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b)
Mean
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c)
Median
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d)
Median
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e)
Variance
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f)
Variance
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g)
Standard
deviation
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h)
Standard
deviation
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i)
From above computed
results from Train A and Train B, what train should be preferred and why?
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41. Use
the information from the problem number 5 on page 3-21 to fill in the given
table below and answer the following questions (a-h) (**Using D-method).
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Number of miles flown
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Number of frequent
Flyers (f)
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CF
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MidPoint
(x)
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d
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fd
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d2
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fd2
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(1,000)
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-1
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0
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1
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2
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3
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4
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Total
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a)
Find mean
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b)
Find median
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c)
Find mode
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d)
Find Range
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e)
Find variance
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f)
Find standard deviation
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g)
Find 1st
Quartile
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h)
Find 99th
percentile
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42. Use
the information from the problem number 1 on page 3-39 to fill in the given
table below and answer the following questions (a-h) (**Using D-method).
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Dinner Check
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Frequency
(f)
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CF
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MidPoint
(x)
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d
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fd
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d2
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fd2
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($)
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-2
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-1
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0
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1
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2
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3
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Total
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a)
Find mean
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b)
Find median
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c)
Find mode
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d)
Find Range
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e)
Find variance
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f)
Find standard deviation
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g)
Find 3rd Quartile
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h)
Find 80th percentile
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43. The
mean GMAT score of 65 applicants who were accepted into the MBA program of
Xavier Business School was 520 with variance of 225. About how many applicants scored between 470
and 570 on the GMAT?
44. Work
on problem number 11 on page 3-49 (a-b).
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a)
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b)
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45. Use
the information from the problem number 2 on page 4-8 and answer the following
questions (a-h); Given that Y = Income rate and X = Average expense
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a)
Find
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b)
Find
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c)
Interpret the meaning of
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d)
Find the regression
equation
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e)
Predict the income rate
for an area with an average expense of $75
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f)
Compute the coefficient
of determination
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g)
Interpret the coefficient
of determination
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h)
Compute and interpret the
coefficient of correlation
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46. An
educator wants to see how strong the relationship is between a student’s score
on a test and his or her grade-point average. The data obtained from the sample
are shown.
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Test Score (X)
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98
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105
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100
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100
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106
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95
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116
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112
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GPA (Y)
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2.1
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2.4
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3.2
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2.7
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2.2
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2.3
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3.8
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3.4
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a)
Find
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b)
Find
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c)
Interpret the meaning of
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d)
Find the regression
equation
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e)
Predict the GPA for a
student who gets 145 in the test score.
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f)
Compute the coefficient
of determination
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g)
Interpret the coefficient
of determination
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h)
Compute and interpret the
coefficient of correlation
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47. Please
use the given printout and answer the following questions.
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SUMMARY OUTPUT
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Regression
Statistics
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Multiple R
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0.190885429
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R Square
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0.036437247
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Adjusted R Square
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-0.44534413
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Standard Error
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2.502630195
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Observations
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4
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ANOVA
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df
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SS
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MS
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F
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Significance F
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Regression
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1
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0.473684211
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0.47368421
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0.0756303
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0.809114571
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Residual
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2
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12.52631579
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6.26315789
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Total
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3
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13
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Coefficients
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Standard Error
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t Stat
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P-value
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Lower 95%
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Upper 95%
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Intercept
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2.894736842
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1.904216054
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1.52017248
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0.2678372
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-5.298443561
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11.08792
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X Variable
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-0.315789474
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1.148285486
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-0.2750095
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0.8091146
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-5.256463153
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4.624884
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a)
What is
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b)
What is
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c)
Interpret the meaning of
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d)
What is the regression
equation
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e)
What is the coefficient
of determination
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f)
What is the coefficient
of correlation
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g)
Interpret the coefficient
of determination
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h)
Interpret the coefficient
of correlation
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48. From
the below cross classification showing the frequencies of hair and eye color of
a group of students at North Texas, and answer the following questions (a-d).
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Eye Color
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|||||
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Hair Color Blond
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Brown
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Blue
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Green
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Hazel
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Total
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Blond
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30
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18
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7
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2
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57
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Brown
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74
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28
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10
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7
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119
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Red/Auburn
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17
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15
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5
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3
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40
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Black
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43
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11
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6
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1
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61
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Total
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164
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72
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28
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13
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277
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a)
Probability that a
student will have blue eyes given he/she is blond.
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b)
Probability
of black hair.
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c)
Probability
that a student will have either red hair or green eyes.
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d)
Probability
that a student will have brown hair and brown eyes.
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49. Work
on problem number 33 on page 5-19 (a-d)
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a)
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b)
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c)
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d)
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50. Work
on problem number 17 on page 5-16 (a-e)
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a)
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b)
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c)
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d)
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e)
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