251x0312 9/23/03
ECO251 QBA1
FIRST HOUR EXAM
October 1, 2003
Name: _____________________
Social Security Number: _____________________
Part I.
(32 points)
1.
The process of using sample statistics to draw conclusions about true population parameters is
called
a) statistical inference.
b) the scientific method.
c) sampling.
d) descriptive statistics.
2.
A summary measure that is computed to describe a characteristic of an entire population is called
a) a parameter.
b) a census.
c) a statistic.
d) the scientific method.
3.
Which of the following is a discrete quantitative variable?
a) the Dow Jones Industrial Average
b) the volume of water released from a dam
c) the distance you drove yesterday
d) the number of employees of an insurance company
TABLE 1-1
The manager of the customer service division of a major consumer electronics company is interested in determining
whether the customers who have purchased a videocassette recorder made by the company over the past 12 months are
satisfied with their products.
4.
Referring to Table 1-1, the possible responses to the question "Are you happy, indifferent, or
unhappy with the performance per dollar spent on the videocassette recorder?, " if we write down a
1 for ‘happy, ’ a 2 for ‘unhappy’ and a 3 for ‘indifferent, are the following kind of random
variable.
a) ratio
b) nominal
c) interval
d) ordinal
1
251x0312 9/23/03
TABLE 2-2
At a meeting of information systems officers for regional offices of a national company, a survey was taken to
determine the number of employees the officers supervise in the operation of their departments, where X is the
number of employees overseen by each information systems officer.
X
f_
1
7
2
5
3
11
4
8
5
9
5.
Referring to Table 2-2, how many regional offices are represented in the survey results?
a) 127
b) 5
c) 15
d) 40
TABLE 2-5
The following are the durations (in minutes) of a sample of long-distance phone calls made within the continental
United States, reported by one long-distance carrier:
Time (in Minutes)
0 but less than 5
5 but less than 10
10 but less than 15
15 but less than 20
20 but less than 25
25 but less than 30
30 but less than 35
Relative
Frequency
0.37
0.22
0.15
0.10
0.07
0.07
0.02
6.
Referring to Table 2-5, if 1,000 calls were randomly sampled, how many calls lasted under 10
minutes?
a) 220
b) 370
c) 410
d) 590
7.
If I make a graph of the data in table 2-5 (Assume the table represents a sample of 1000 calls) with
the following x and y coordinates for the first five points: {(0, 0), (5, 370), (10, 590), (15, 740) ,
(20, 840)}, a one-word name for this type of graph is __________ , and the last point on the line
could be (45, _____ )
8.
Referring to Table 2-5, what is Frel for the percentage of calls that lasted under 20 minutes?
a) 0.10
b) 0.76
c) 0.84
d) None of the above – write in the correct answer.
2
251x0312 9/23/03
TABLE 2-7
The stem-and-leaf display below contains data on the number of months between the date a civil suit is filed and
when the case is actually adjudicated for 50 cases heard in superior court.
Stem
Leaves
1
234447899
2
22223455678889
3
0011135778
4
02345579
5
112466
6
158
9.
Referring to Table 2-7, the civil suit with the fourth shortest waiting time between when the suit
was filed and when it was adjudicated had a wait of ________ months.
10. Eunice computes the following statistics from a sample
 x  x 
n
(n  1)( n  2)
 x  x 
3
,
k3
s3
,


x  x 4 3n  13 s 4 
n2
3mean  mode 
n  1
 . She
, k4 


std .deviation
n 1
n  1n  2n  3 
n
n2


thinks the sample represents a population that is skewed to the right. Which of the statistics would
show skewness and what sign should she expect from them? (No partial credit on this one.)
2
,
11. In a perfectly symmetrical distribution with one mode.
a) the arithmetic mean equals the median.
b) the median equals the mode.
c) the arithmetic mean equals the mode.
d) all of the above.
e) none of the above.
12. According to the Bienayme-Chebyshev rule (I called it Chebyshef’s Inequality), at least 93.75% of
all observations in any data set are contained within a distance of how many standard deviations
around the mean?
a) 1
b) 2
c) 3
d) 4
13. Evaluate the following statements. (i) The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 4.05.
(ii) In a set of numerical data , the value for Q3 can never be smaller than the value for Q1. (iii) In
a set of numerical data, the value for Q2 is always halfway between Q1 and Q3.
a) (i) and (ii) are false.
b) (i) and (iii) are false.
c) (ii) and (iii) are false
d) Only one of the statements is false.
e) All of the statements are false.
3
251x0312 9/23/03
14. Which one of the following statements is false?
a) In a sample of size 40, the sample mean is 15. In this case, the sum of all observations in
x  600 .
the sample is

b) A population with 200 elements has an arithmetic mean of 10. From this
information, it can be shown that the population standard deviation is 15.
c) The median of a data set with 20 items would be the average of the 10th and 11th items in
the ordered array.
d) The coefficient of variation measures variability in a data set relative to the size of the
arithmetic mean.
e) If every group of 10 individuals in the population is equally likely to be chosen to be in
the sample, we must be taking a simple random sample of 10.
f) All of the above statements are false.
15. Which of the following is NOT a measure of central tendency?
a) the arithmetic mean
b) the geometric mean
c) the mode
d) the interquartile range
16. Which of the following is most sensitive to extreme values?
a) the median
b) the interquartile range
c) the arithmetic mean
d) the 1st quartile
4
251x0312 9/23/03
Part II. (Ng pp 77-79) (8 points)
The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal. It is a
x  217 ,
x 2  4541
sample containing 11 numbers. Note:


{11, 15, 23, 29, 19, 22, 21, 20, 15, 25, 17}
Find:
a) The First Quartile (1.5)
b) The Standard Deviation (2)
c) The Coefficient of variation (1.5)
d) The five-number summary (3)
5
251x0312 9/23/03
ECO251 QBA1
FIRST EXAM
October 1, 2003
TAKE HOME SECTION
Name: _________________________
Social Security Number: _________________________
Throughout this exam show your work! Please indicate clearly what sections of the problem you are
answering and what formulas you are using.
Part III. Do all the Following (11 Points) Show your work!
1. My Social Security Number is 265398248. If I use each digit as a frequency in and the intervals below, I
get:
Class
$0- 5999
$6000- 11999
$12000- 17999
$18000- 23999
$24000- 29999
$30000- 35999
$36000- 41999
$42000- 47999
$48000- 53999
Frequency
2
6
5
3
9
8
2
4
8
Replace my Social Security number with your own in the frequency column. To make the problem easier,
you may replace all zeros in your new frequency column with 10s.
Assume that this data represents a sample of rents paid in Chester County.
a. Calculate the Cumulative Frequency (0.5)
b. Calculate The Mean (0.5)
c. Calculate the Median (1)
d. Calculate the Mode (It is possible but unlikely that there is more than one)(0.5)
e. Calculate the Variance (1.5)
f. Calculate the Standard Deviation (1)
g. Calculate the Interquartile Range (1.5)
h. Calculate a Statistic showing Skewness and Interpret it (1.5)
i. Make a frequency polygon of the Data (Neatness Counts!)(1)
j. Extra credit: Put a (horizontal) box plot below the histogram using the same scale. (1)
6
251x0312 9/23/03
2. My Social Security Number is 265398248. If I write it in clumps of 2 numbers and add 100 to the end, I
get:
26, 53, 98, 24, 8, 100.
Write your social security number the same way, so that you have a list of six numbers. Note: If any of these
five numbers is a zero, change it to a one. For these five numbers, compute the a) Geometric Mean b)
Harmonic mean, c) Root-mean-square (1point each). Label each clearly. If you wish, d) Compute the
geometric mean using natural or base 10 logarithms. (1 points extra credit each ).
7