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STA 225:
Test 1
Theo Ogunyemi
Name ______________________________
Winter 2004
Attempt all questions. Except for multiple choice questions, show all your work to get full
credit. For problems in Part II, only final answer with no work shown worth zero points. Please
be precise and to the point. Good Luck.
PART I (Multiple Choice, 2 points each)
1. The average monthly salary of all female workers is $40,000. The average salary of all male
workers is $44,000. What must be true about the average salary of all workers?
A)
B)
C)
D)
It must be $42,000.
It must be larger than the median salary.
It could be any number between $40,000 and $44,000.
It must be larger than $42,000.
2. A sample of five recent births at a local hospital yielded birth-weights (in ounces) of
79
132
127
132
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The median birth weight in this sample is
A)
B)
C)
D)
112.
132.
127.
141.
3. A set of data has a mean that is much smaller than the median. Which of the following
statements is most consistent with this information?
A)
B)
C)
D)
A histogram of the data is symmetric.
A histogram of the data is skewed left.
A histogram of the data is skewed right.
The data set probably has a few low outliers .
4. There are five children in a room, ages three, four, five, six and seven. If a five-year old
child enters the room the
A)
B)
C)
D)
mean age will stay the same, but the variance will increase.
mean age will stay the same, but the variance will decrease.
mean age and variance will stay the same.
mean age and variance will increase.
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5. The standard deviation of 16 measurements of people’s weights (in pounds) is
computed to be 6.2. The variance of these measurements is
A)
B)
C)
D)
38.44.
29.16.
52.34.
2.49
6. The standard deviation of 16 measurements of people’s weights (in pounds) is
computed to be 6.2. The units for the variance of these measurements is
A)
B)
C)
D)
pounds squared.
square root pounds.
pounds.
no units. Variance never has units.
7. A smooth curve that approximates the shape of a histogram and describes the overall
pattern of a distribution is called a
A)
B)
C)
D)
density curve.
timeplot.
normal plot.
histogram.
8. The household income in a certain community is normally distributed with a mean of
$42,000 and a standard deviation of $5,000. The proportion of households with incomes
exceeding $47,000 is
A)
B)
C)
D)
0.1587.
0.8413.
1.0000.
0.4207.
9. A market research company employs a large number of typists to enter data into a computer.
The time taken for new typists to learn the computer system is known to have a normal
distribution with a mean of 90 minutes and a standard deviation of 18 minutes. The
proportion of new typists that take over an hour to learn the computer system is
A)
B)
C)
D)
0.952.
0.548.
0.048.
0.452.
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10. Two variables are said to be positively associated if
A) above average values of one variable tend to accompany below average values of
the other.
B) above average values of one variable tend to accompany above average values of
the other.
C) below average values of one variable tend to accompany below average values of
the other.
D) below average values of one variable can be accompanied by either above or below
average values of the other.
E) B and C
11. The correlation coefficient measures
A)
B)
C)
D)
whether there is a relation between two variables.
whether or not a scatterplot shows an interesting pattern.
whether a cause and effect relation exists between two variables.
the strength of a straight line relation between two variables.
12. Which of the following is true of the coefficient of determination?
A) It is a measure of nonlinear association between X and Y.
B) -1 ≤ r 2 ≤ 1.
C) If r is the correlation between X and Y, r 2 is the correlation between Y 2 and
X 2.
€ €It is the percent of variation in Y that is accounted for by X.
€ D)
€
€
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PART II (Show all your work to get full credit. Be precise and to the point.)
1. (25 pts.) The following are the IQ’s of 16 applicants to an undergraduate engineering
program.
111
108
106
110
125
112
108
104
115
112
109
128
107
106
109
111
(a) Draw a stemplot of the data. Give comments.
(b) Construct a frequency/relative frequency/cumulative relative frequency table for the data.
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(c) Construct a relative frequency histogram for the data. Give comments.
(d) Are there possible outliers in the data set? If yes, identify them.
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2. (21pts) The following data give the weights (in pounds) lost by 15 members of a health
club at the end of two months after joining the club.
5
10
8
7
25
12
5
14
11
10
21
9
8
11
(a)
Compute the mean and standard deviation of the data.
(b)
Calculate the 5-number summary.
(c)
Which of the two sets of statistics, ( x,s) or 5-number summary, is more
appropriate to describe the data set given in part (a), and why?
€
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3. (20pts) IQ scores for school children are standardized so that they are approximately
normally distributed with a mean of 100 and a standard deviation of 15.
(a)
What is the random variable in this problem?
(b)
What is the probability that a randomly selected child has an IQ of less than 80?
(c)
What is the probability that a randomly selected child has an IQ of between 85
and 110?
(d)
What percent of the school children have IQ scores that are at least 120?
(e)
How high must a child’s IQ score be in order to belong to the top 10% of the
group?
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4 (30pts) A chemical company, wishing to study the effects of extraction time on the efficiency
of an extraction operation, obtained the data shown in the following table:
Extraction time (minutes)
X 27 41 19 35 39 19 49 31
______________________________________________________
Extraction efficiency (%)
Y 57 80 46 62 72 52 77 68
(a)
Draw a scatterplot of the data.
(b) Calculate the correlation between X and Y, using the data above.
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(c) Calculate the best prediction equation.
(d) Plot the least square line on the scatterplot above.
(e) Predict the extraction efficiency (%) when the extraction time is 40 minutes.
(f) What percent variation in extraction efficiency is accounted for by the extraction time?
(g) Is the best prediction equation obtained in part (c) above, a good one? Why or why not?