TA Review
2004.11.10
Chapter 2
1. Below you are given the examination scores of 20 students.
52 99 92 86 84
63 72 76 95 88
92 58 65 79 80
90 75 74 56 99
a. Construct a frequency distribution for this data. Let the first class be 50 – 59
and draw a histogram.
b. Construct a cumulative frequency distribution.
c. Construct a relative frequency distribution.
d. Construct a cumulative relative frequency distribution.
ANSWERS:
Score
50 60 70 80 90 Total
59
69
79
89
99
Freq.
3
2
5
4
6
20
Cumul.
Freq.
3
5
10
14
20
Relative
Freq.
0.15
0.10
0.25
0.20
0.30
1.00
Cumul.
Relative
Freq.
0.15
0.25
0.50
0.70
1.00
2. The SAT math scores of a sample of business school students and their genders are
shown below.
SAT Math Scores
Gender Less than 400 400 up to 600 600 and more Total
Female 24
168
48
240
Male
40
96
24
160
Total 64
264
72
400
a.
How many students scored less than 400?
b.
How many students were female?
c.
Of the male students, how many scored 600 or more?
d.
Compute row percentages and comment on any relationship that may exist
between SAT math scores and gender of the individuals.
e.
Compute column percentages.
ANSWERS:
a.
64
b.
240
c.
24
1
d.
SAT Math Scores
Gender
Less than 400 400 up to 600 600 and more Total
Female
10%
70%
20%
100%
Male
25%
60%
15%
100%
From the above percentages it can be noted that the largest percentages of both
genders' SAT scores are in the 400 to 600 range. However, 70% of females and
only 60% of males have SAT scores in this range. Also it can be noted that
10% of females' SAT scores are under 400, whereas, 25% of males' SAT scores
fall in this category.
e.
SAT Math Scores
Gender
Less than 400 400 up to 600 600 and more
Female
37.5%
63.6%
66.7%
Male
62.5%
36.4%
33.3%
Total
100%
100%
100%
Chapter 3
1. A sample of 9 mothers was taken. The mothers were asked the age of their oldest
child. You are given their responses below.
a.
b.
c.
d.
e.
f.
g.
h.
3 12 4 7 14 6 2 9 11
Compute the mean.
Compute the variance.
Compute the standard deviation.
Compute the coefficient of variation.
Determine the 25th percentile.
Determine the median
Determine the 75th percentile.
Determine the range.
2. The following data represent the daily demand (y in thousands of units) and the unit
price (x in dollars) for a product.
Daily Demand (y)
47
39
35
44
34
20
15
30
Unit Price (x)
1
3
5
3
6
8
16
6
2
a. Compute and interpret the sample covariance for the above data.
b. Compute and interpret the sample correlation coefficient.
ANSWERS:
-160.14 (rounded). Since the covariance is negative, it indicates a negative
relationship between x and y.
-0.922. There is a strong negative relationship between daily demand and unit price.
Chapter 4
1. A machine is used in a production process. From past data, it is known that 97% of
the time the machine is set up correctly. Furthermore, it is known that if the machine
is set up correctly, it produces 95% acceptable (non-defective) items. However, when
it is set up incorrectly, it produces only 40% acceptable items.
a. An item from the production line is selected. What is the probability that the selected
item is non-defective?
b. Given that the selected item is non-defective, what is the probability that the machine
is set up correctly?
c. What method of assigning probabilities was used here?
ANSWERS:
a. 0.9335
b. 0.9871
c. the relative frequency method
3