Download Chapter 3: Self Practice Questions

Chapter 3: Self Practice Questions
Note: These questions are not meant to be an exhaustive representation of the
material you will see on exams or quizzes. They are designed to help you
familiarize yourself with the material. These questions are neither submitted
nor graded.
Calculations
1. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th,
25th, 65th, and 75th percentiles.
2. J. D. Powers and Associates surveyed cell phone users in order to learn about the minutes of cell
phone usage per month (Associated Press, June 2002). Minutes per month for a sample of 15
cell phone users are shown here.
615
135
395
430
830
1180
690
250
420
265
245
210
180
380
105
a.
b.
c.
d.
What is the mean number of minutes of usage per month?
What is the median number of minutes of usage per month?
What is the 85th percentile?
J. D. Powers and Associates reported that the average wireless subscriber plan allows up
to 750 minutes of usage per month. What do the data suggest about cell phone
subscribers’ utilization of their monthly plan?
3. Millions of Americans get up each morning and telecommute to work from offices in their home.
Following is a sample of age data for individuals working at home.
18 54 20 46 25 48 53 27 26 37
40 36 42 25 27 33 28 40 45 25
a. Compute the mean and mode.
b. The median age of the population of all adults is 35.5 years (The World Almanac, 2004).
Use the median age of the preceding data to comment on whether the at-home workers
tend to be younger or older than the population of all adults.
c. Compute and interpret the first and third quartiles.
4. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range,
interquartile range, variance, and standard deviation.
5. Car rental rates per day for a sample of seven eastern U.S. cities are as follows (The Wall Street
Journal, January 16, 2004).
City
Daily Rate ($)
Boston 43
Atlanta 35
Miami 34
New York 58
Orlando 30
Pittsburgh 30
Washington, D.C. 36
a. Compute the mean, variance, and standard deviation for the car rental rates.
b. A similar sample of seven western U.S. cities showed a sample mean car rental rate of $38
per day. The variance and standard deviation were 12.3 and 3.5, respectively. Discuss any
difference between the car rental rates in eastern and western U.S. cities.
6. The Energy Information Administration reported that the mean retail price per gallon of regular
grade gasoline was $1.47 (The Wall Street Journal, January 30, 2003). Suppose that the standard
deviation was $.08 and that the retail price per gallon has a bell-shaped distribution.
a. What percentage of regular grade gasoline sold between $1.39 and $1.55 per gallon?
b. What percentage of regular grade gasoline sold between $1.39 and $1.63 per gallon?
c. What percentage of regular grade gasoline sold for more than $1.63 per gallon?
7. A department of transportation’s study on driving speed and mileage for midsize automobiles
resulted in the following data.
Driving Speed: 30 50 40 55 30 25 60 25 50 55
Mileage:
28 25 25 23 30 32 21 35 26 25
Compute and interpret the sample correlation coefficient.
8. The following is a frequency distribution of grades for a statistics examination.
Examination Grade
Frequency
40  49
3
50  59
5
60  69
11
70  79
22
80  89
15
90  99
6
Treating these data as a sample, compute the following:
a.
The mean
b.
The standard deviation
c.
The variance
d.
The coefficient of variation
Multiple Choice
1. The mean of a sample is
a.
b.
c.
d.
always equal to the mean of the population
always smaller than the mean of the population
computed by summing the data values and dividing the sum by (n
computed by summing all the data values and dividing the sum by the number of items
2. After the data has been arranged from smallest value to largest value, the value in the middle is
called the
a. Range
b. Median
c. Mean
d. None of the other answers are correct.
3. The value of the sum of the squared deviations from the mean, i.e., ( x  x)2 must always be
a.
b.
c.
d.
less than the mean
negative
either positive or negative depending on whether the mean is negative or positive
at least zero
4. Which of the following is not a measure of dispersion?
a. the range
b. the 50th percentile
c. the standard deviation
d. the interquartile range
Table 1
A researcher has collected the following sample data. The mean of the sample is 5.
3
5
12
3
2
5. Refer to Table 1. The variance is
a. 80
b. 4.062
c. 13.2
d. 16.5
6. Refer to Table 1. The standard deviation is
a. 8.944
b. 4.062
c. 13.2
d. 16.5
7. Suppose annual salaries for sales associates from a particular store have a bell-shaped
distribution with a mean of $32,500 and a standard deviation of $2,500. The z-score for a sales
associate from this store who earns $37,500 is
a. 37.5
b. 2
c. -2
d. 0.92
8. For data skewed to the left, the skewness is
a. between 0 and .5
b. less than 1
c. positive
d. negative
ANSWER to calculation questions
1. Using the method described in the book (not Excel)
20th percentile: 20.0
25th percentile: 22.5
65th percentile: 28.0
75th percentile: 29.0
2.
a. 422
b. 380
c. 690
d. Both the mean and median usage is well below the 750 minutes usage. In fact 85% of the
customers use 690 minutes or less. With the exception of one customer that clearly goes over
the allotted usage (1130 minutes per month) everybody else seems to be below or slightly
above (830) of the plan’s allowance.
3.
a. Sample mean = 34.75
Mode = 25 (appears three times)
b. Median = 34.5
At-home workers are slightly younger.
c. First quartile: 25.5
Third quartile: 43.5
4. Range = 19
IQR = 6.5
Sample mean = 25.5
Sample variance = 34.57
Sample std. dev. = 5.88
5.
a. Mean = 38
Sample Variance = 97
Sample Std. Dev. = 9.85
b. Eastern shows more variation
6.
a. 68%
b. 81.5%
c. 2.5%
7. Correlation Coef. = -0.91; strong negative relationship
8.
a. 74.016
b. 12.601
c. 158.778
d. 17.02%
ANSWER to multiple choice questions
d, b, d, b, d, b, b ,d