Research Methods and Statistics A Critical Thinking Approach, 4th Edition by Sherri L. Jackson – Test Bank

 

Instant Download – Complete Test Bank With Answers

 

 

Sample Questions Are Posted Below

 

Chapter 5

Data Organization and Descriptive Statistics

Chapter Outline

 

Organizing Data
Frequency Distributions
Graphs
Bar Graphs and Histograms
Frequency Polygons
Descriptive Statistics
Measures of Central Tendency
Mean
Median
Mode
Measures of Variation
Range
Average Deviation and Standard Deviation
Types of Distributions
Normal Distributions
Kurtosis
Positively Skewed Distributions
Negatively Skewed Distributions
z-scores
z-scores, the Standard Normal Distribution, Probability, and Percentile Ranks
Summary

 

Review of Key Terms

 

Average Deviation—An alternative measure of variation that, like the standard deviation, indicates the average difference between the scores in a distribution and the mean of the distribution.

 

Bar Graph—A graphical representation of a frequency distribution in which vertical bars are centered above each category along the x-axis and are separated from each other by a space indicating that the levels of the variable represent unrelated and distinct categories.

 

Class Interval Frequency Distribution—A table in which the scores are grouped into intervals and listed along with the frequency of scores in each interval.

 

Descriptive Statistics—Numerical measures that describe a distribution by providing information on the central tendency of the distribution, the width of the distribution, and the shape of the distribution.

 

Frequency Distribution—A table in which all of the scores are listed along with the frequency with which each occurs.

 

Frequency Polygon— A line graph of the frequencies of individual scores.

 

Histogram— A graphical representation of a frequency distribution in which vertical bars centered above scores on the x-axis touch each other to indicate that the scores on the variable represent related, increasing values.

 

Kurtosis—How flat or peaked a normal distribution is.

 

Leptokurtic—Normal curves that are tall and thin with only a few scores in the middle of the distribution having a high frequency.

 

Mean—A measure of central tendency; the arithmetic average of a distribution.

 

Measure of Central Tendency—A number intended to characterize an entire distribution.

 

Measure of Variation— A number that indicates how dispersed scores are around the mean of the distribution.

 

Median—A measure of central tendency; the middle score in a distribution after the scores have been arranged from highest to lowest or lowest to highest.

 

Mesokurtic—Normal curves that have peaks of medium height and distributions that are moderate in breadth.

 

Mode—A measure of central tendency; the score in a distribution that occurs with the greatest frequency.

 

Negatively Skewed Distribution—A distribution in which the peak is to the right of the center point and the tail extends toward the left, or in the negative direction.

 

Normal Curve—A symmetrical, bell-shaped frequency polygon representing a normal distribution.

 

Normal Distribution—A theoretical frequency distribution having certain special characteristics.

 

Percentile Rank—A score that indicates the percentage of people who scored at or below a given raw score.

 

Platykurtic—Normal curves that are short and more dispersed (broader).

 

Positively Skewed Distribution— A distribution in which the peak is to the left of the center point and the tail extends toward the right, or in the positive direction.

 

Probability—The expected relative frequency of a particular outcome.

 

Qualitative Variable—A categorical variable for which each value represents a discrete category.

 

Quantitative Variable—A variable for which the scores represent a change in quantity.

 

Range—A measure of variation; the difference between the lowest and the highest score in a distribution.

 

Standard Deviation—A measure of variation; the average difference between the scores in the distribution and the mean or central point of the distribution, or more precisely, the square root of the average squared deviation from the mean.

 

Standard Normal Distribution—A normal distribution with a mean of 0 and a standard deviation of 1.

 

Variance—The deviation squared.

 

z-score (Standard Score)—A number that indicates how many standard deviation units a raw score is from the mean of a distribution.

 

 

Relevant Articles from Handbook for Teaching Statistics and Research Methods (1st ed.)

 

Beins, B. Teching the relevance of statistics through consumer-oriented research. Pp. 5-6.

 

Dillbeck, M. C. Teaching statistics in terms of the knower. Pp. 20-23.

 

Dillon, K. M. Statisticophobia. P. 3.

 

Forsyth, G. A. A task-first individual-differences approach to designing a statistics and methodology course. Pp. 15-17.

 

Hastings, M. W. Statistics: Challenge for students and the professor. Pp. 6-7.

 

Jacobs, K. W. Instructional techniques in the introductory statistics course: The first class meeting. P. 4.

 

Magnello, M. E., & Spies, C. J. Using organizing concepts to facilitate the teaching of statistics. Pp. 12-15.

 

Shatz, M. A. The Greyhound strike: Using a labor dispute to teach descriptive statistics. P. 35.

 

Ward, E. F. Statistics mastery: A novel approach. Pp. 17-20.

 

 

Relevant Articles from Handbook for Teaching Statistics and Research Methods (2nd ed.)

 

Beins, B. A BASIC program for generating integer means and variances. Pp. 9-10.

 

Pittenger, D. J. Teaching students about graphs. Pp. 16-20.

 

 

Web Resources

For step-by-step practice and information, have your students check out the Statistics and Research Methods Workshops at www.cengage.com/psychology/workshops. In addition, practice quizzes, vocabulary flashcards, and more are available at www.cengage.com/psychology/jackson.

 

 

Answers to Chapter Exercises

 

1. Speed                           f                       rf        

62                            1                     .05

64                            3                     .15

65                            4                     .20

67                            3                     .15

68                            2                     .10

70                            2                     .10

72                            1                     .05

73                            1                     .05

76                            1                     .05

79                            1                     .05

                80                            1                     .05        

20                   1.00

 

2. Interval                        f                       rf        

61-62                        1                     .05

63-64                        3                     .15

65-66                        4                     .20

67-68                        5                     .25

69-70                        2                     .10

71-72                        1                     .05

73-74                        1                     .05

75-76                        1                     .05

77-78                        0                     .00

                79-80                        2                     .10        

20                   1.00

 

3. Either a histogram or a frequency polygon could be used to graph these data. However, due to the continuous nature of the speed data, a frequency polygon might be most appropriate. Both a histogram and a frequency polygon of the data are presented.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4. = 68.55

Md = 67

Mo = 65

The distribution is positively skewed.

 

5. a.  = 7.3

Md = 8.5

Mo = 11

 

4.  = 4.83

Md = 5

Mo = 5

 

6.  = 6.17

Md = 6.5

Mo = 3, 8

 

5.  = 5.5

Md = 6

Mo = 6

 

6. a. range = 8
   s = 2.74

s = 2.58

AD = 2.22

 

2. range = 8
   s = 2.74

            s = 2.58

AD = 2.22

 

27. range = 80
    s = 27.4

            s = 25.8

AD = 22.2

 

1. range = .80
   s = .274

            s = .258

AD = .222

 

273. range = 800
     s = 273.86

            s = 258.20

            AD = 222.22

 

7. a. z = +2.57

Proportion of cars that cost an equal amount or more = .0051

 

2. z = ­-2.0

Proportion of cars that cost and equal amount or more = .9772

 

2. z = +2.0

Percentile rank = 97.72

 

3. z = -3.14

Percentile rank = .08

 

3. z = -3.14, z = +2.0

Proportion between = .4992 + .4772 = .9764

 

1. 16^th percentile converts to a z-score of -.99

-.99(3500) + 23,000 = $19,535

 

8. a. z = +1.33

Proportion drinking equal to or more = .0918.

 

2. z = -2.0

Proportion drinking equal to or more = .9772.

 

2. z = -2.0, z = +1.33

Proportion between = .4772 + .4082 = .8854.

 

1. 60^th percentile converts to a z-score of +.25

.25(1.5) + 5 = 5.375 cups.

 

1. z = -.67

Percentile rank = 25.14

 

1. z = +1.67

Percentile rank = 95.25

 

9.

                           x                   z-score             percentile rank

 

      Ken             73.00                    ­.22                      41.29

Drew           88.95                +1.55                      93.94

Cecil           83.28                  +.92                     82.00

 

 

Test Items

 

Multiple Choice Questions

 

1. A table in which all of the scores are listed along with the frequency with which each occurs is a _____.
   a. bar graph
   b.      histogram
   c.      frequency polygon
   d.      frequency distribution

Answer: d

 

^w2. A table in which the scores are grouped into intervals and listed along with the frequency of scores in each interval is a _____.
a.      bar graph
b.      histogram
c.      class interval frequency distribution
d.      class interval frequency polygon

Answer: c

 

3. A categorical variable for which each value represents a discrete category is a _____ variable.
   a. qualitative
   b.      quantitative
   c.      continuous
   d.      class interval

Answer: a

 

4. A variable for which the scores represent a change in quantity is a _____ variable.
   a. qualitative
   b.      quantitative
   c.      class interval
   d.      nominal

Answer: b

 

5. A graphical representation of a frequency distribution in which vertical bars are centered above each category along the x-axis and are separated from each other by a space, is a _____.
   a. histogram
   b.      bar graph
   c.      pie graph
   d.      frequency polygon

 

Answer: b

6. A graphical representation of a frequency distribution in which vertical bars centered above scores on the x-axis touch each other is a _____.
   a.      histogram
   b.      bar graph
   c.      pie graph
   d.      frequency polygon

 

Answer: a

 

^w7. A line graph of the frequencies of individual scores is a _____.
a.      histogram
b.      frequency distribution
c.      frequency polygon
d.      bar graph

 

Answer: c

 

8. _____ is to organizing data using a table as _____ is to organizing data using a figure.
   a. histogram; bar graph
   b.      frequency polygon; bar graph
   c.      frequency distribution; histogram
   d.      frequency polygon; frequency distribution

 

Answer: c

9. Bar graphs are to _____ as frequency polygons are to _____.
   a. quantitative variables; qualitative variables
   b.      qualitative variables; quantitative variables
   c.      continuous data; discrete data
   d.      quantitative variables and continuous data; qualitative variables and discrete data

Answer: b

 

10. Qualitative variable is to quantitative variable as ____ is to _____.
    a. categorical variable; numerical variable
    b. numerical variable; categorical variable
    c.      ordinal, interval, or ratio data; nominal data
    d.      categorical variable and ordinal, interval, or ratio data; numerical variable and nominal data

Answer: a

 

11. A number that characterizes the “middleness” of an entire distribution is _____.
    a. a measure of central tendency
    b. a measure of variability
    c.      an inferential statistic
    d.      the standard deviation

Answer: a

 

^w12. The arithmetic average of a distribution is the:
a.      mean
b.      median
c.      mode
d.      standard deviation

Answer: a

 

13. Seven students reported the following individual earnings from their sale of wrapping paper: $7, $13, $3, $5, $2, $9, and $3. In this distribution of individual earnings, the mean is _____ the mode and _____ the median.
    a. equal to; equal to
    b.      greater than; equal to
    c.      equal to; less than
    d.      greater than; greater than

Answer: d

 

^w14.  During the past year, Cindy and Bobby each read 2 books, but Greg read 25, Jan read 12, and Marcia read 9.  The median number of books read by these individuals was:
a.      2.
b.      9.
c.      10.
d.      50.

Answer: b

 

15. The middle score in a distribution after the scores have been arranged from highest to lowest or lowest to highest is the _____.
    a. mean
    b. median
    c.      mode
    d.      standard deviation

Answer: b

 

16. When Ms. Jones calculated her students’ accounting test scores, she noticed that one student had an extremely low score. Which measure of central tendency should not be used in this situation?
    a. mean
    b.      standard deviation
    c.      mode
    d.      median

Answer: a

 

17. Imagine that 86,999 people who are penniless live in Centerville. Bill Gates, whose net worth is $87,000,000,000 moves to Centerville. Now the mean net worth in this town is _____ and the median net worth is _____.
    a. 0; 0
    b. 0; $1,000,000
    c.      $1,000,000; 0
    d.      $1,000,000; $1,000,000

Answer: c

 

18. Arithmetic average is to _____ as score occurring with the greatest frequency is to _____.
    a. mean; median
    b. median; mode
    c.      mean; mode
    d.      mode; median

Answer: c

 

^w19.        Mode is to _____ as median is to _____.
a.      interval and ratio data only; nominal data only
b.      nominal data only; ordinal data only
c.      all types of data; ordinal, interval, and ratio data only
d.      none of the alternative is correct

Answer: c

 

20. A distribution can have more than one ____ but can have only one _____.
    a. median; mode or mean
    b. mean; mode or median
    c.      mode; median or mean
    d.      median or mode; mean

Answer: c

 

21. Which of the following is a disadvantage of using the range as a measure of variation?
    a. It is limited because only two of the scores in the distribution are used to derive it.
    b. It is easily distorted by an unusually high or low score in a distribution.
    c.      It can only be used with nominal data.
    d.      It is limited because only two of the scores in the distribution are used to derive it and it is
    easily distorted by an unusually high or low score in a distribution.

 

Answer: d

22. The calculation of the average deviation differs from the calculation of the standard deviation in that the difference scores are:
    a. squared.
    b. converted to absolute values.
    c.      squared and converted to absolute values.
    d.      it does not differ.

 

Answer: b

23. Imagine that distribution A contains the following scores: 3, 4, 5, 6, 7. Imagine that distribution B contains the following scores: 1, 3, 5, 8, 10. Distribution A has a _____ standard deviation and a _____ average deviation in comparison to distribution B.
    a. larger; larger
    b. smaller; smaller
    c.      larger; smaller
    d.      smaller; larger

 

Answer: b

24. Which of the following is NOT TRUE?
    a. The range is a simplistic measure of variation that does not use all scores in the distribution
    in its calculation.
    b.      The average deviation is a more sophisticated measure of variation than the range in which
    all scores are             used, but which may not weight extreme scores adequately.
    c.      The standard deviation is the least sophisticated measure of variation and the least
    frequently used.
    d.      All of the alternatives are true.

 

Answer: c

^w25.  If the shape of a frequency distribution is lopsided, with a long tail projecting longer to the right than to the left, how would the distribution be skewed?
a.      normally
b.      negatively
c.      positively
d.      average

 

Answer: c

26. A z-score is most affected by the:
    a. median
    b. mode
    c.      standard deviation
    d.      range

 

Answer: c

27. If Joe scored 25 on a test with a mean of 20 and a standard deviation of 5 what is his z-score?
    a. 25
    b. +1.0
    c.      0.0
    d.      cannot be determined

 

Answer: b

28. Sue took a test in both biology and math last week. The biology test had a mean of 70 and a standard deviation of 7 whereas the math test had a mean of 75 and a standard deviation of 10. Sue scored a 76 on the biology test and a 76 on the math test. On which test did she do better in comparison to the rest of the class?
    a. the math test
    b. the biology test
    c.      she did the same on each test
    d.      cannot be determined

 

Answer: b

 

^W29. Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What proportion of faculty consume an amount between 4 and 6 cups?
a.      .5468
b.      .4972
c.      .50
d.      none of the alternative is correct

 

Answer: b

30. Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What is the percentile rank for an individual who consumed 8 cups of coffee per day?
    a. 97.72
    b. 2.28
    c.      47.72
    d.      none of the alternatives is correct

 

Answer: a

 

31. Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. How many cups of coffee would an individual at the 25^th percentile drink per day?
    a. 4
    b. 5
    c.      6
    d.      7

 

Answer: a

32. If the average height for women is normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches, then approximately 95% of all women should be between _____ and _____ inches in height.
    a. 62.5; 67.7
    b. 60; 70
    c.      57.5; 72.5
    d.      Cannot say from the information given.

 

Answer: b

 

^w33. Rich’s first psychology exam score is +1 standard deviation from the mean in a normal distribution. The test has a mean of 60 and a standard deviation of 6. Rich’s percentile rank would be approximately:
a.      70%.
b.      84%.
c.      66%.
d.      Cannot say from the information given.

 

Answer: b

 

34. Approximately what percentage of scores are between z=1 and z=2?
    a. 50
    b. 68
    c.      16
    d.      13.5

 

Answer: d

 

35. Karen’s first psychology exam score is ‑1 standard deviation from the mean in a normal distribution. The test has a mean of 75 and a standard deviation of 5. Karen’s percentile rank would be:
    a. 16%.
    b. 54%.
    c.      70%.
    d.      cannot say from the information given

 

Answer: a

 

36. In a psychology class of 100 students, test scores are normally distributed with a mean of 80 and a standard deviation of 5. Approximately what percentage of students have scores between 70 and 90?
    a. 68%
    b. 80%
    c.      95%
    d.      99%

 

Answer: c

 

Short Answer/Essay Questions

 

1. Draw the frequency polygon for the following sample distribution (there are 30 scores in the distribution). In addition calculate the mean, median and mode for the distribution.

48, 50, 53, 59, 59, 63, 63, 67, 67, 67, 72, 72, 72, 78, 78, 78, 78, 85, 85, 85, 85, 85, 90, 90, 90, 90,
95, 95, 98, 100

 

 

 

 

2. Explain the difference between qualitative and quantitative variables noting the relationship of nominal, ordinal, interval, and ratio data to these terms.

A qualitative variable is a categorical variable for which each value represents a discrete category, whereas a quantitative variable is a variable for which the scores represent a change in quantity. Nominal data are qualitative and ordinal, interval, and ration data are quantitative.

 

3. Explain the difference in proper use between a bar graph and a histogram.

 

A bar graph is used when the data are nominal and qualitative. A histogram is used when the data are qualitative and ordinal, interval, o ratio.

 

4. Calculate the mean, median, and mode for the following sample: 2, 2, 6, 9, 10, 11, 15, 17, 18, 20.

   The mean is 11, the median is 10.5, and the mode is 2.

 

5. For a hypothetical normal distribution of test scores, approximately 95% fall between 38 and 62, 2.5% are below 38 and 2.5% are above 62. Given this information, (a) the mode = _________ and (b) the standard deviation = _________.

   The mode is 50 (along with the mean and median) and the standard deviation is 6.

 

6. Calculate s (standard deviation) and A.D. (average deviation) for the following sample.
   2, 2, 6, 9, 10, 10, 15, 18, 18, 20.

   The standard deviation is 6.56 and the A.D. is 5.4.

 

 

7. Draw a positively skewed distribution and a negatively skewed distribution noting where the mean, median, and mode would fall with respect to each other in these distributions.

• Negatively Skewed Positively Skewed

8. Tom, Tina, & Tori took a verbal aptitude test. The test was normally distributed with a mean of 70 and s = 15. Complete the following table.

Name               Raw Score                    Z score             Percentile Rank

 

Tom                      73                                 +.20                         57.93

 

Tina                      52                              -1.2                           11.51

 

Tori                       58.9                             –.74                         23

 

9. Students in the psychology department consume
   an average of 5 cups of coffee per day with a standard deviation of 1.75 cups. The number of cups of coffee consumed is normally distributed.

• What proportion of students consume an amount equal to or less than 6 cups per day?

  .7157

• How many cups would an individual at the 80^th percentile drink?

  47

 

10. Draw two distributions with the same standard deviations but different means.