Download Chapters 1 to 3

Test Items for Explaining Psychological Statistics, 2e
by Barry Cohen
Chapter 1
Introduction to Psychological Statistics
Section A
1. The term "statistics " refers to:
a) values derived from the data in a sample
b) facts expressed in numerical form
c) a branch of mathematics
*d) all of the above
2. Subjects are randomly assigned to watch either a horror movie or a comedy, and the amount
of popcorn they eat during the movie is measured. For this experiment, the type of movie is:
* a) an independent variable
b) a dependent variable
c) a continuous variable
d) a constant
3. A group of habitual coffee drinkers is compared to a group of subjects who do not drink
coffee in terms of average sleep latency over a one-month period. This study is an example of:
a) experimental research
* b) correlational research
c) descriptive research
d) statistical research
4. Self-esteem is an example of:
a) an experimental variable
b) an ordinal variable
* c) a continuous variable
d) a discrete variable
5. A parameter is based on the values in:
a) an experiment
b) a random sample
* c) a population
d) a ratio scale
6. If all of the variables in your study have been measured on a nominal scale:
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Chapter 1
Test Items
a) your study is not a true experiment
b) you can only use descriptive statistics
c) you can only use parametric statistics
* d) you can only use nonparametric statistics
7. You can use parametric statistics only if at least one of your variables has been measured on:
a) a nominal scale
b) a discrete scale
c) an ordinal scale
* d) an interval scale
8. Even if your data consist of numbers, it is not valid to perform arithmetic operations on those
numbers, if your data were derived from:
* a) a nominal scale
b) a discrete scale
c) a ratio scale
d) an interval scale
9. Psychological variables, such as anxiety or creativity, are not likely to be measured:
a) on an ordinal scale
b) in terms of numbers
* c) on a ratio scale
d) as a continuous variable
10. If a subject's attitude towards the death penalty is assessed on a scale that consists of:
strongly opposed, somewhat opposed, slightly opposed, neutral, slightly for, somewhat for, and
strongly for, which of the following types of scales is being used?
a) a nominal scale
* b) an ordinal scale
c) an interval scale
d) a ratio scale
Section B
Install Equation Editor and doubleclick here to view equation.
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Chapter 1
Test Items
a) 7 b) 27 c) 49 d) 140
-12. Given the following set of numbers: 1, 3, 3, 5, 28, what is the value of Σ(5X-1)?
a) 44 b) 160 c) 195 d) 199
-13. Given the following set of numbers: 1, 3, 3, 5, 28, what is the value of Σ(X)2?
a) 40 b) 784 c) 828 d) 1600
-14. Given the following set of numbers: 1, 3, 3, 5, 28, what is the value of ΣX2?
a) 40 b) 784 c) 828 d) 1600
-15. Given that: X1 = 3, X2 = 6, X3 = 9, Y1 = 4, Y2 = 8, Y3 = 12, what is the value of ΣXY?
a) 42 b) 84 c) 168 d) 432
-16. Given that: X1 = 3, X2 = 6, X3 = 9, Y1 = 4, Y2 = 8, Y3 = 12, what is the value of (ΣX)(ΣY)?
a) 42 b) 84 c) 168 d) 432
-17. Given that: X1 = 3, X2 = 6, X3 = 9, Y1 = 4, Y2 = 8, Y3 = 12, what is the value of Σ(2X+Y)?
a) 60 b) 168 c) 336 d) 864
-18. Given that: X1 = 3, X2 = 6, X3 = 9, Y1 = 4, Y2 = 8, Y3 = 12, what is the value of Σ(X+Y)2?
a) 242 b) 350 c) 686 d) 1764
-19. Round off 5.9962 to two decimal places:
a) 5.99 b) 5.996 c) 6.0 d) 6.00
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Chapter 1
Test Items
-20. Round off 36.666 to one decimal place:
a) 36.6 b) 36.7 c) 37 d) 40
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Chapter 2
Frequency Tables, Graphs, and Distributions
Section A
1. If your data have been measured on an ordinal scale, the most appropriate way to display the
distribution is by means of:
a) a frequency polygon
b) a histogram
* c) a bar graph
d) an ogive
2. The largest cumulative frequency in a cumulative frequency distribution is equal to:
a) 1.0
b) 100
* c) N
d) N/100
3. To convert a cumulative frequency to a cumulative percentage, you can multiply the cf by:
a) 100
b) N
c) N/100
* d) 100/N
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4. The first quartile always equals:
* a) the score whose percentile rank is 25
b) the score whose percentile rank is N/25
c) .25N
d) 4N/100
5. As you move to the right on a cumulative frequency polygon, the line on the graph:
a) always slopes upward
* b) never slopes downward
c) never reaches N
d) eventually intersects the horizontal axis
6. The points of the cumulative frequency polygon for a grouped distribution are placed directly
over:
a) the upper limit of each interval
* b) the upper real limit of each interval
c) the lower real limit of each interval
d) the midpoint of each interval
7. The points of the frequency polygon for a grouped distribution are placed directly over:
a) the upper limit of each interval
b) the upper real limit of each interval
c) the lower real limit of each interval
* d) the midpoint of each interval
8. All of the entries in a cumulative percentage column are:
* a) percentile ranks
b) percentiles
c) deciles
d) upper real limits
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9. The width of a class interval in a grouped distribution is always exactly equal to:
a) the upper apparent limit minus the lower apparent limit
* b) the upper real limit minus the lower real limit
c) the range of scores divided by the number of intervals
d) all of the above
10. When choosing the limits of the lowest interval in a grouped frequency distribution, which
of the following conditions is desirable?
* a) the upper apparent limit is a multiple of the class width
b) the upper real limit is a multiple of the class width
c) the lower real limit is a multiple of the class width
d) the upper apparent limit of the lowest interval is lower than the lowest score in the
distribution
Section B
The list of numbers below represents the number of cats owned by a sample of individuals who
attended a cat show:
1, 2, 1, 2, 0, 3, 2, 2, 5, 1, 1, 1, 4, 3, 0, 2, 1, 4, 3, 0.
Create a frequency distribution for these data, and refer to it when answering Questions 11, 12,
and 13.
11. What is the percentile rank of someone who owns three cats?
a) 15 b) 30 c) 70 d) 85
-12. How many cats do you need to own to be at the 45th percentile?
a) 0 b) 1 c) 2 d) 3
-13. What percentage of the sample owns three or more cats?
a) 15 b) 30 c) 70 d) 85
-14. What is the width of a class interval whose apparent limits range from 3.6 to 4.0?
a) .4 b) .5 c) .6 d) .05
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15. If you are dealing with reaction time data in milliseconds, and the numbers range from 320
to 760, which of the following would be the most recommended as the width of the class
intervals in a grouped frequency distribution?
a) 10 b) 20 c) 25 d) 50
-16. Assume that a 2000-pound car gets a gas mileage of 30 mpg, while a 3000-pound car gets 20
mpg. Using linear interpolation, what would be the gas mileage for a car that weighs 2200
pounds?
*
a) 22
b) 24
c) 26
d) 28
17. Suppose that for heart rate 81 bpm is at the 70th percentile, while 85 bpm is at the 78th
percentile. Using linear interpolation, what is the percentile rank corresponding to a heart rate of
82 bpm?
*
a) 70.3
b) 70.8
c) 72.0
d) 72.4
18. Suppose that for heart rate 81 bpm is at the 70th percentile, while 85 bpm is at the 78th
percentile. Using linear interpolation, what heart rate (in bpm) is at the 76th percentile?
*
a) 81.25
b) 81.75
c) 84.25
d) 84.75
The following grouped frequency distribution represents the data from a group of men on a
reduced-fat diet. Refer to this distribution when answering Questions 19 through 25.
Weight (pounds)
210 - 219
200 - 209
190 - 199
180 - 189
170 - 179
Frequency
1
3
3
4
6
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160 - 169
150 - 159
140 - 149
130 - 139
120 - 129
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7
5
2
1
19. What is the relative frequency associated with the interval from 170 to 179?
a) .12 b) .15 c) .30 d) 6
-20. What weight corresponds to a cumulative relative frequency of .7?
a) 150 b) 179.5 c) 184.5 d) 195
-21. What is the percentile rank of a man who weighs 159.5 pounds?
a) 7 b) 15 c) 30 d) 37.5
-22. What is the percentile rank of a man who weighs 172 pounds?
a) 50.75 b) 57.5 c) 57.75 d) 61.25
-23. What weight is at the 20th percentile?
a) 145 b) 149.5 c) 155 d) 159.5
-24. What weight is at the third quartile?
a) 150 b) 179.5 c) 184.5 d) 195
-25. What weight is at the median of the distribution?
a) 164.5
--
b) 165.75 c) 166.25 d) 169.5
Section C
26. Compared to a grouped frequency distribution, a
stem-and-leaf display of the same data will always:
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Chapter 3
*
a) contain fewer scores
b) contain fewer intervals
c) contain more information
d) make it easier to find percentiles and percentile ranks
27. If you rotate a stem-and-leaf display so that the stem is horizontal, it will resemble:
*
a) a bar graph
b) a frequency polygon
c) an ogive
d) a bell curve
28. Suppose that you are constructing a stem-and-leaf display for a set of IQ scores. According
to the most likely scheme for the stems, what would be used as the stem for a score of 118?
a) 1
--
b) 11
c) 18 d) 8
29. Suppose that you are constructing a stem-and-leaf display for the weights (in pounds) of a
group of students. If the weights range from 93 to 176 pounds, how many stems would you be
likely to use?
a) 7
b) 8
c) 9
--
d) 10
30. A major advantage of the stem-and-leaf plot as compared to other methods for displaying
data is that:
*
a) all of the original data are preserved
b) any skewing of the distribution will be evident
c) it takes up less space
d) it displays data horizontally rather than vertically
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Chapter 3
Chapter 3
Measures of Central Tendency and Variability
Section A
1. Central Tendency refers to:
*
a) the tendency of one statistic to be used more than others
b) the tendency for most of the values in a distribution to cluster near the middle
c) the value that most tends to be at the center of a distribution
d) the likelihood that a distribution will have a single midpoint
2. Which of the following cannot be used (validly) with ordinal data?
* a) the mean
b) the median
c) the mode
d) none of the above (i.e., all can be used)
3. Which of the following is most likely to be strongly affected by taking an extreme
point and making it even more extreme?
* a) the mean
b) the median
c) the mode
d) none of the above will be affected.
4. The mode:
a) is the number of times the most frequent value appears in the distribution
* b) is equal to the value that appears most often in a distribution
c) is equal to the value that is in the middle of the distribution
d) is the number of times the middle value of a distribution appears in the distribution
5. The median:
a) is the value that appears most often in a sample
* b) is the value that is larger than half the values in a distribution, and smaller than half
the values
c) is the value that is half of the distance between the smallest and largest values in
the distribution
d) is equal to half of the sum of all of the scores in a distribution divided by the
number of scores
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6. The sum of the absolute values of the deviations is smallest when the deviations are
taken from:
a) the mode
* b) the median
c) the mean
d) it depends on the shape of the distribution
7. The sum of the squared deviations is smallest when the deviations are taken from:
a) the mode
b) the median
* c) the mean
d) it depends on the shape of the distribution
8. A distribution can have more than one:
* a) mode
b) median
c) mean
d) mode, median, or mean
9. If all of the scores in a distribution are multiplied by the same constant:
* a) the mean will be multiplied by that constant
b) the mean will be divided by that constant
c) the mean will be equal to that constant
d) the mean will be unchanged
10. In a positively-skewed distribution, the median will be:
a) above the 50th percentile
b) below the 50th percentile
* c) at the 50th percentile
d) greater than zero
11. In a negatively-skewed distribution, the mean will be:
a) above the 50th percentile
* b) below the 50th percentile
c) at the 50th percentile
d) less than zero
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12. It is not possible for more than half of the scores in a distribution to be above:
a) the mode
* b) the median
c) the mean
d) the mode, median, or mean
13. Which of the following is likely to give rise to a negatively skewed distribution?
a) a very difficult exam
b) a reaction-time experiment
c) a floor effect
* d) a ceiling effect
14. If the mean is larger than the median for a particular distribution:
a) a calculation error has been made
b) all the scores must be greater than zero
* c) the distribution must be positively skewed
d) there is probably a ceiling effect
15. Which of the following is unaffected by extreme scores?
a) the range
* b) the interquartile range
c) the mean deviation
d) the standard deviation
16. Which of the following can be applied to ordinal data?
* a) the interquartile range
b) the mean deviation
c) the standard deviation
d) the variance
17. The semi-interquartile range is equal to half the distance:
a) of the range
b) from the first percentile to the 99th percentile
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c) from the 10th percentile to the 90th percentile
* d) from the 25th percentile to the 75th percentile
18. The sum of all of the deviations from the mean:
a) is always positive
b) is always negative
* c) is always zero
d) depends on the number of scores
19. The sum of squares (SS) is equal to:
*
a) the square of the population variance
b) the square-root of the population variance
c) the population variance multiplied by the number of values
d) the sum of the squared scores
20. If all of the scores in a distribution are the same:
a) the standard deviation will be negative
* b) the standard deviation will be equal to zero
c) the standard deviation will be undefined
d) the standard deviation will reach infinity
21. If all of the scores in a distribution are multiplied by the same constant:
* a) the standard deviation will be multiplied by that constant
b) the standard deviation will be divided by that constant
c) the standard deviation will be equal to that constant
d) the standard deviation will be unchanged
22. If all of the scores in a distribution are divided by the same constant:
a) the variance will be multiplied by that constant
b) the variance will be divided by that constant
* c) the variance will be divided by the square of that constant
d) the variance will be unchanged
23. If the same constant is subtracted from all of the scores in a distribution:
a) the standard deviation will be negative
b) that constant will be subtracted from the standard deviation
c) that constant will be added to the standard deviation
* d) the standard deviation will be unchanged
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24. The standard deviation:
a) is always equal to the mean deviation
b) is never equal to the mean deviation
c) is never larger than the mean deviation
* d) is never smaller than the mean deviation
25. The difference between the biased and unbiased sample variances:
a) increases as the number of scores increases
* b) decreases as the number of scores increases
c) decreases as the sum of squares increases
d) none of the above
Section B
The next three questions refer to the following set of scores:
1, 5, 5, 8, 9, 10, 11
26. What is the mean for the data set above?
a) 5 b) 7 c) 7.5 d) 8
-27. What is the median for the data set above?
a) 5 b) 7 c) 7.5 d) 8
-28. Based on the mean and median of the data set above, what can you say about the
distribution of those data?
*
a) The distribution is positively skewed
b) The distribution is negatively skewed
c) The distribution is symmetrical
d) The distribution is bimodal
29. What is the mean of the following set of numbers:
-8, -7, -7, 0, +3, +7?
a) 0 b) +6.4 c) -2.4 d) -2.0
-30. What is the median of the following set of numbers:
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Chapter 3
-19, -7, -6, 0, +2, +4?
a) -3 b) -6 c) 0 d) +3
-31. What is the mode of the following set of numbers:
-9, -2, -2, -1, 0, 0, 0, +2, +2, +5, +6, +7, +8, +9?
a) +1 b) +2 c) 0 d) +.5
-32. Before conducting a maze-learning experiment you weigh two groups of rats. The
experimental group, which contains 20 rats, has an average weight of 18 ounces, while
the control group, which contains 10 rats, has an average weight of 15 ounces.
What would the average weight be if the two groups of rats were combined into one large
group?
a) 16 b) 16.5 c) 17 d) 18
-33. Imagine that a friend of yours has earned 24 credits of A's, 12 credits of B's, and 12
credits of C's. If an A is worth 4 points, a B = 3 points, and a C = 2 points, what is your
friend's GPA? [Hint: take a weighted average of the point values for A, B, and C].
a) 3.0 b) 3.25 c) 3.33 d) 3.5
-34. If you know that the 25th percentile of a distribution is 17, and the 75th percentile is
33, what is the value for the semi-interquartile range?
* a) 8
b) 16
c) 25
d) cannot be determined from the information given
35. Given the following set of numbers: 1, 3, 3, 5, 28, what is the value for the sum of
squares (SS)?
a) 320 b) 508 c) 828 d) 1600
-36. Given the following set of numbers: 1, 3, 3, 5, 28, what is the value for the variance
(σ2)?
a) 101.6 b) 508 c) 828 d) 1600
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37. For the following set of numbers: 2, 4, 5, 6, 13, what is the value for the mean
deviation?
a) 0 b) 2.33 c) 2.8 d) 3.33
-38. For the following set of numbers: 2, 4, 5, 6, 13, what is the (approximate) value for
the (unbiased) standard deviation?
a) 3.7 b) 4.2 c) 8.4 d) 17.5
-39. If the population variance formula has been used on a sample of 10 subjects, and σ2 =
27, what would be the value for the unbiased variance (s2) measured for the same 10
subjects?
a) 24.3 b) 27 c) 30 d) 33
-40. If the unbiased standard deviation has been calculated for a sample of 12 subjects,
and s = 3, what would be the value for the sum of squares (SS) measured for the same 10
subjects?
a) 33 b) 36 c) 99 d) 108
-Section C
41. One of the most important purposes of a box-and-whisker plot is:
a) to show, in a comprehensible way, the location of all of the scores in a
distribution
*
b) to identify outliers
c) to provide a quick and easy way to identify percentiles
d) to display data that were measured on a nominal (i.e., categorical) scale
42. The distance between the inner fences is how many times the H-spread?
a) 1.0 b) 1.5 c) 3.0 d) 4.0
-43. The box-and-whisker plot is based on which measure of central tendency?
a) the mode
*
b) the median
c) the mean
d) it depends on the nature of the data
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44. In a box-and-whisker plot, the whiskers are drawn horizontally in each direction until
they reach the:
*
a) adjacent values
b) inner fences
c) hinges
d) nearest outlier
45. If outliers are expected, which of the following procedures can be planned to deal
with the problem?
a) trimming
b) Winsorizing
c) a data transformation
*
d) all of the above
46. The first step in calculating kurtosis is to take the deviations from the mean and:
a) square each of them
b) cube each of them
c) take the cube-root of each of them
*
d) raise each to the fourth power
47. Suppose that the weight in pounds is measured for each individual in the population
of adult males, and the skewness of the distribution turns out to be +2. If weight is
transformed to kilograms by dividing each man's weight by 2.2, what will be the
skewness of the new distribution?
*
a) +.9
b) +2
c) +2.2
d) +4.4
48. If the mean of a distribution is below the median, the skewness of the distribution
will be:
*
a) negative
b) positive
c) zero
d) less than 1.0
49. The t distribution is leptokurtic. This means that large samples from the t
distribution will tend to have a value for kurtosis that is:
*
a) negative
b) positive
c) zero
d) less than 1.0
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50. If the kurtosis calculated for a large sample is -2.5, what does this suggest about the
population distribution from which the sample was drawn?
*
a) it probably has relatively thin tails
b) it is probably platykurtic
c) it is probably not a normal distribution
d) all of the above
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