Review Questions 2

Review Questions

Complete the following exercises from “Review Questions” located at the end of each chapter and put them into a Word document to be submitted as directed by the instructor.

Chapter 1, numbers 1.8 and 1.9

Chapter 2, numbers 2.14, 2.17, and 2.18

Chapter 3, numbers 3.13, 3.14, 3.18, and 3.19

Chapter 4, numbers 4.9, 4.14, 4.17, and 4.19

Show all relevant work; use the equation editor in Microsoft Word when necessary.

1.8 Indicate whether each of the following studies is an experiment or an observational study. If it is an experiment, identify the independent vari-able and note any possible confounding variables.

(a) A psychologist uses chimpanzees to test the notion that more crowded living conditions trigger aggressive behavior. Chimps are placed, accord-ing to an impartial assignment rule, in cages with either one, several, or many other chimps. Subsequently, during a standard observation period, each chimp is assigned a score based on its aggressive behavior toward a chimplike stuffed doll.

(b) An investigator wishes to test whether, when compared with recognized, professional scientists, recognized, professional artists tend to be born under different astrological signs.

(c) To determine whether there is a relationship between the sexual codes of primitive tribes and their behavior toward neighboring tribes, an anthro-pologist consults available records, classifying each tribe on the basis of its sexual codes (permissive or repressive) and its behavior toward neigh-boring tribes (friendly or hostile).

(d) In a study of group problem solving, an investigator assigns college stu-dents to groups of two, three, or four students and measures the amount of time required by each group to solve a complex puzzle.

(e) A school psychologist wishes to determine whether reading comprehension scores are related to the number of months of formal education, as reported on school transcripts, for a group of 12-year-old migrant children. Copyright © 2015 John Wiley & Sons, Inc. REVIEW QUESTIONS 23

(f) To determine whether Graduate Record Exam (GRE) scores can be increased by cramming, an investigator allows college students to choose to participate in either a GRE test-taking workshop or a control (non-test-taking) workshop and then compares the GRE scores earned subsequently by the two groups of students.

(g) A social scientist wishes to determine whether there is a relationship between the attractiveness scores (on a 100-point scale) assigned to college students by a panel of peers and their scores on a paper-and-pencil test of anxiety.

(h) A political scientist wishes to determine whether males and females differ with respect to their attitudes toward defense spending by the federal

government. She asks each person if he or she thinks that the current level of defense spending should be increased, remain the same, or be decreased.

1.9 Recent studies, as summarized, for example, in E. Mortensen et al. (2002). The association between duration of breastfeeding and adult intelligence. Journal of the American Medical Association, 287 , 2365–2371, suggest that breast-feeding of infants may increase their subsequent cognitive ((IQ) development. Both experiments and observational studies are cited. (a ) What determines whether some of these studies are experiments? (b) Name at least two potential confounding variables controlled by breast-feeding experiments. 1.10 If you have not done so already, familiarize yourself with the various appendices in this book. (a) Particularly note the location of Appendix B (Answers to Selected Ques-tions) and Appendix D (Glossary). (b) Browse through Appendix A (Math Review). If this material looks unfamil-iar, study Appendix A and use the self-diagnostic tests as your guides. Copyright © 2015 John Wiley & Sons, Inc.

(f) To determine whether Graduate Record Exam (GRE) scores can be increased by cramming, an investigator allows college students to choose to participate in either a GRE test-taking workshop or a control (non-test-taking) workshop and then compares the GRE scores earned subsequently by the two groups of students.

(g) A social scientist wishes to determine whether there is a relationship between the attractiveness scores (on a 100-point scale) assigned to col-lege students by a panel of peers and their scores on a paper-and-pencil test of anxiety.

(h) A political scientist wishes to determine whether males and females differ with respect to their attitudes toward defense spending by the federal government. She asks each person if he or she thinks that the current level of defense spending should be increased, remain the same, or be decreased.

1.9 Recent studies, as summarized, for example, in E. Mortensen et al. (2002). The association between duration of breastfeeding and adult intelligence. Journal of the American Medical Association, 287 , 2365–2371, suggest that breast-feeding of infants may increase their subsequent cognitive ((IQ) development. Both experiments and observational studies are cited.

(a ) What determines whether some of these studies are experiments? (b) Name at least two potential confounding variables controlled by breast-feeding experiments.

REVIEW QUESTIONS 2.14

(a) Construct a frequency distribution for the number of difference residences occupied by graduating seniors during their college career, namely

1, 4, 2, 3, 3, 1, 6, 7, 4, 3, 3, 9, 2, 4, 2, 2, 3, 2, 3, 4, 4, 2, 3, 3, 5

(b) What is the shape of this distribution?

2.15 The number of friends reported by Facebook users is summarized in the following frequency distribution:

FRIENDS f

f400 – above 2

350 – 399 5

300 – 349 12

250 – 299 17

200 – 249 23

150 – 199 49

100 – 149 27

50 – 99 29

0 – 49 36

Total 200

(a) What is the shape of this distribution?

(b) Find the relative frequencies.

(c) Find the approximate percentile rank of the interval 300–349.

(d) Why would it not be possible to convert to a stem and leaf display?

2.16

Assume that student volunteers were assigned arbitrarily (according to a coin toss) either to be trained to meditate or to behave as usual. To deter-mine whether meditation training (the independent variable) influences GPAs (the dependent variable), GPAs were calculated for each student at the end of the one-year experiment, yielding these results for the two groups:

NONMEDITATORS

3.67 3.79 3.00

2.50 2.75 1.90

2.80 2.65 2.58

2.83 3.10 3.37

3.25 2.76 2.86

2.90 2.10 2.66

2.34 3.20 2.67

3.59 3.00 3.08

MEDITATORS

3.57 2.45 3.75

3.50 2.67 2.90

2.95 3.30 3.56

3.56 3.78 3.75

3.56 3.78 3.75

3.45 3.00 3.35

3.10 2.75 3.09

2.58 2.95 3.56

3.30 3.43 3.47

DESCRIBING DATA WITH TABLES AND GRAPHS

(a) What is the unit of measurement for these data?

(b) Construct separate frequency distributions for meditators and for non-meditators. (First, construct the frequency distribution for the group having the larger range. Then, to facilitate comparisons, use the same set of classes for the other frequency distribution.)

(c) Do the two groups tend to differ? (Eventually, tools from inferential statistics, as described in Part 2, will help you decide whether any apparent difference between the two groups probably is real or merely transitory, that is, attributable to variability or chance. See Review Question 14.15 on page 324.)

*2.17 Are there any conspicuous differences between the two distributions in the following table (one reflecting the ages of all residents of a small town and the other reflecting the ages of all U.S. residents)?

(a) To help make the desired comparison, convert the frequencies ( f ) for the small town to percentages.

(b) Describe any seemingly conspicuous differences between the two distributions.

TWO AGE DISTRIBUTIONS

U.S. POPULATION (2010) (%)13,5,6,7,7,7,7,6,7,7,7,7,7, population Total-100%

AGE 65–above 60-64,55-59,50-54,45-49,40-44,65-39,30-34,25-29,20-24,15-19,

10-14,5-9,0-4

SMALL TOWN f 105,53,45,40,44,38,31,27,25,20,20,19,17,16 TOTAL 500

NOTE: The top class (65–above) has no upper boundary. Although less preferred, as discussed previously, this type of open-ended class is employed as a space-saving device when, as in the Statistical Abstract of the United States, many different tables must be listed. Source: 2012 Statistical Abstract of the United States.Copyright © 2015 John Wiley & Sons, Inc.

REVIEW QUESTIONS 55 (c) Using just one graph, construct frequency polygons for the two relative frequency distributions. NOTE: When segmenting the horizontal axis, assign the same width to the open-ended interval (65–above) as to any other class interval. (This tactic causes some distortion at the upper end of the histogram, since one class interval is doing the work of several. Nothing is free, including the convenience of open-ended intervals.)

2.18 The following table shows distributions of bachelor’s degrees earned in 2005–2006 for selected fields of study by all male graduates and by all female graduates.

(a) How many female psychology majors graduated in 2005–2006?

(b) Since the total numbers of male and female graduates are fairly different— 504,600 and 676,000—it is helpful to convert fi rst to relative frequencies before making comparisons between male and female graduates. Then, inspect these relative frequencies and note what appear to be the most conspicuous differences between male and female graduates.

(c) Would it be meaningful to cumulate the frequencies in either of these frequency distributions?

(d) Using just one graph, construct bar graphs for all male graduates and for all female graduates. Hint: Alternate shaded and unshaded bars for males and females, respectively.

BACHELOR’S DEGREES EARNED IN 2005–2006

BY SELECTED FIELD OF STUDY AND GENDER

(IN THOUSANDS)

MAJOR FIELD OF STUDY

MALES 159.7 80.8 12.9 19.9 67.0 26.7 32.1 51.2 28.1 37.7 17.3 Tot.504.6

FEMALES158.4 80.7 79.1 68.3 14.6 42.5 51.2 48.8 9.8 37.8 Tot.676.0

Business

Social sciences

Education Health

Sciences

Psychology

Engineering

Life sciences

Fine arts

Communications

Computer sciences

English 17.3 37.8 Total 504.6 676.0

3.14 The mean serves as the balance point for any distribution because the sum of all scores, expressed as positive and negative distances from the mean, always equals zero.

(a) Show that the mean possesses this property for the following set of scores: 3, 6, 2, 0, 4.

(b) Satisfy yourself that the mean identifies the only point that possesses this property. More specifically, select some other number, preferably a whole number (for convenience), and then find the sum of all scores in Part (a) expressed as positive or negative distances from the newly selected number. This sum should not equal zero.

3.15 If possible, find the median for the fi lm ratings listed in Question 2.8 on page 39.

3.16 Specify the single average—the mode, median, or mean—described by the following statements.

(a) It never can be used with qualitative data.

(b) It sometimes can be used with qualitative data.

(c) It always can be used with qualitative data.

(d) It always can be used with ranked data.

(e) Strictly speaking, it only can be used with quantitative data.

3.17 Indicate whether each of the following distributions is positively or negatively skewed. The distribution of

(a) incomes of taxpayers has a mean of $48,000 and a median of $43,000

(b) GPAs for all students at some college has a mean of 3.01 and a median of 3.20

(c) number of “romantic affairs” reported anonymously by young adults has a mean of 2.6 affairs and a median of 1.9 affairs

(d) daily TV viewing times for preschool children has a mean of 55 minutes and a median of 73 minutes REVIEW QUESTIONS 73

3.18 Given that the mean equals 5, what must be the value of the one missing observation from each of the following sets of observations?

(a) 1, 2, 10

(b) 2, 4, 1, 5, 7, 7

(c) 6, 9, 2, 7, 1, 2

3.19 Indicate whether the following terms or symbols are associated with the population mean, the sample mean, or both means.

(a) N

(b) varies

(c) S

(d) n (e) constant

(f) subset

REVIEW QUESTIONS *4. 9

For each of the following pairs of distributions, first decide whether their standard deviations are about the same or different. If their standard deviations are different, indicate which distribution should have the larger standard deviation. Hint: The distribution with the more dissimilar set of scores or individuals should produce the larger standard deviation regard-less of whether , on average, scores or individuals in one distribution differ from those in the other distribution.

(a) SAT scores for all graduating high school seniors (a 1 ) or all college fresh-men (a 2 )

(b) Ages of patients in a community hospital (b 1 ) or a children’s hospital (b 2 )

(c) Motor skill reaction times of professional baseball players (c 1 ) or college students (c 2 )

(d) GPAs of students at some university as revealed by a random sample (d 1 ) or a census of the entire student body (d 2 )

(e) Anxiety scores (on a scale from 0 to 50) of a random sample of college students taken from the senior class (e 1 ) or those who plan to attend an anxiety-reduction clinic (e 2 )

(f) Annual incomes of recent college graduates (f 1 ) or of 20-year alumni (f 2 )

4.10 When not interrupted artificially, the duration of human pregnancies can be described, we’ll assume, by a mean of 9 months (270 days) and a standard deviation of one-half month (15 days).

(a) Between what two times, in days, will a majority of babies arrive?

(b) A small minority of all babies will arrive sooner than ______? (c) A small minority of all babies will arrive later than ______?

(d) In a paternity suit, the suspected father claims that since he was overseas during the entire 10 months prior to the baby’s birth, he could not possibly be the father. Any comment?

DESCRIBING VARIABILITY

4.14

(a) Using the computation formula for the sample sum of squares, verify that the sample standard deviation, s , equals 23.33 lbs for the distribution of 53 weights in Table 1.1.

(b) Verify that a majority of all weights fall within one standard deviation of the mean (169.51) and that a small minority of all weights deviate more than two standard deviations from the mean.

4. 17 Why can’t the value of the standard deviation ever be negative?

4.19

Referring to Review Question 2.18 would you describe the distribution of majors for all male graduates as having maximum, intermediate, or minimum variability?