- A researcher is interested in the effect type of residence has on the personal hap-piness of college students. She selects samples of students who live in campus dorms, in off-campus apartments, and at home and asks the 12 respondents to rate their happiness on a scale of 1 (not happy) to 10 (happy).
a. Test the null hypothesis that happiness does not differ by type of residence.
Ho: Happiness does not differ by type of residence
Ha: Happiness differs by type of residence
| Dorms | Apartments | At Home | |
| 8 | 2 | 5 | |
| 9 | 1 | 4 | |
| 7 | 3 | 3 | |
| 8 | 3 | 4 | |
- b. Construct a multiple comparison of means by Tukey’s method to determine precisely where the significant differences occur.
We reject the null hypothesis. There is enough evidence to conclude that there is statisti-cally significant difference among the group.
- A pediatrician speculated that frequency of visits to her office may be influenced by type of medical insurance coverage. As an exploratory study, she randomly chose 15 patients: 5 whose parents belong to a health maintenance organization (HMO), 5 whose parents had traditional medical insurance, and 5 whose parents were un-insured.
- Using the frequency of visits per year from the following table, test the null hypothesis that type of insurance coverage has no effect on frequency of visits.
Ho: Type of insurance coverage is independent of frequency of visits
Ha: Type of insurance coverage is dependent on frequency of visits
HMO Traditional None
b. Conduct a multiple comparison of means by Tukey’s method to determine exactly where the significant differences occur
We fail to reject Ho and conclude that type of insurance coverage is independent of fre-quency
- Using the following random sample of death records by neighborhood type, test the null hypothesis that life expectancy in years does not vary by socioeconomic condition of a neighborhood.
| Subsidized Hous- | Working-Class | Middle-Class |
| ing | Neighborhood | Neighborhood |
| 74 | 82 | 89 |
| 64 | 71 | 70 |
| 73 | 76 | 79 |
| 69 | 80 | 87 |
| 73 | 79 | 68 |
Null: The socioeconomic conditions do not affect the life expectancy. (all means are same)
Alternative: The socioeconomic conditions do affect the life expectancy. (at least one mean is different)
- A researcher is interested in the effect of employment on satisfaction with mar-riage. He selects a random sample of 16 married adults who are employed full-time, employed part-time, temporarily unemployed, or chronically unemployed. He asks respondents to rate their satisfaction in marriage on a scale that ranges from
- (very dissatisfied) to 7 (very satisfied).
- Using the following data, test the null hypothesis that employment status does not affect marriage satisfaction.
| Chronically Unem- | ||||
| Employed Full | Employed Part | Temporarily Unem- | ployed | |
| Time | Time | ployed | ||
| 7 | 4 | 5 | 2 | |
| 5 | 6 | 4 | 0 | |
| 7 | 5 | 4 | 3 | |
| 6 | 4 | 5 | 1 | |
- Construct a multiple comparison of means by Tukey’s HSD method to de-termine precisely where the significant differences occur.
- A researcher conducts a study to determine which terrorist organization—Hamas, Hezbollah, or Al Qaeda—poses the greatest threat to innocent civilians. The re-searcher examines 15 randomly selected bombing attacks committed by these or-ganizations and calculates the number of casualties per attack.
- Using the following casualty data, test the null hypothesis that none of these terrorist groups is more threatening than the rest.
| Hamas | Hezbollah | Al Qaeda |
| 6 | 9 | 9 |
| 2 | 10 | 15 |
| 3 | 14 | 16 |
- Construct a multiple comparison of means by Tukey’s HSD method to de-termine precisely where the significant differences occur in Problem 17.
- A researcher wishes to determine whether exercising at least three times a week is more effective than pharmaceuticals (antidepressants) or psychotherapy in ad-dressing mental health issues. He randomly assigns 20 psychiatric patients to one of four treatment conditions and asks their self-reported depression at the moment on a scale of 1 (very depressed) to 15 (very happy). Test the null hypothesis that there is no difference between exercise, antidepressants, therapy, and the control group using the following data.
| Exercise | Antidepressants | Therapy | Control |
| 9 | 9 | 10 | 7 |
| 10 | 10 | 11 | 6 |
| 8 | 14 | 7 | 8 |
| 6 | 11 | 12 | 6 |
| 13 | 9 | 8 | 11 |
Since P-value > 0.05, so at 5% level of significance, we reject the null hypothesis and we can conclude that there is no difference between exercise, antidepressants, therapy and the con-trol group.
| 7. | Does one’s relationship status affect how many vacation days a person takes in a | ||||||||||||||||
| year? | |||||||||||||||||
| a. Using these data collected from samples of adults, test the null hypothesis | |||||||||||||||||
| Ha: | µ | µ | µ | (that status does not affect the number of vacation days taken). | |||||||||||||
| = | = | = | µ | = | µ | ||||||||||||
| Ho: | |||||||||||||||||
| At least one | µ | , is unequal | |||||||||||||||
| Ongoing Rela- | Civil Union/ | Widowed/ | |||||||||||||||
| Single | tionship | Married | Separated | Divorced | |||||||||||||
| 11 | 11 | 16 | 23 | 3 | |||||||||||||
| 13 | 33 | 27 | 2 | 21 | |||||||||||||
| 17 | 24 | 18 | 8 | 13 | |||||||||||||
| 9 | 17 | 9 | 8 | 7 | |||||||||||||
| 23 | 29 | 14 | 9 | 2 | |||||||||||||
| 14 | 23 | 24 | 10 | 14 | |||||||||||||
b. Construct a multiple comparison of means by Tukey’s HSD method to de-termine precisely where the significant differences occur.
There is sufficient evidence that one’s relationship status does affect how many vacations days person takes in a year. The result is statistically significant
- A health researcher is interested in comparing three methods of weight loss: low-calorie diet, low-fat diet, and low-carb diet. He selects 30 moderately overweight subjects and randomly assigns 10 to each weight-loss program. The following weight reductions (in pounds) were observed after a 1-month period:
| Low Calorie | Low Fat | Low Carb |
| 7 | 7 | 7 |
| 3 | 8 | 14 |
| 7 | 8 | 9 |
| 9 | 7 | 10 |
| 5 | 8 | 7 |
| 10 | 10 | 11 |
| 4 | 9 | 8 |
| 5 | 11 | 5 |
| 6 | 5 | 8 |
| 2 | 2 | 6 |
Test the null hypothesis that the extent of weight reduction does not differ by type of weight-loss program.
We fail to reject null hypothesis at 5% level of significance and the extent weight reduction does not differ. Significantly by type of weight loss program
9. Consider an experiment to determine the effects of alcohol and marijuana on driv-ing. Five randomly selected subjects are given alcohol to produce legal drunken-ness and then are given a simulated driving test (scored from a top score of 10 to a bottom score of 0). Five different randomly selected subjects are given marijuana and then the same driving test. Finally, a control group of five subjects is tested for driving while sober.
a. Given the following driving test scores, test for the significance of differ-µ µ µences among means of the following groups:
Ho: = =
| Solutions Manual | Chapter 8: | |||
| Elementary Statistics in Social Research | Analysis of Variance | |||
| Ha:µ ≠µ ≠µ | ||||
| Alcohol | Drugs | Control | ||
| 3 | 1 | 8 | ||
| 4 | 6 | 7 | ||
| 1 | 4 | 8 | ||
| 1 | 4 | 5 | ||
| 3 | 3 | 6 | ||
- Conduct a multiple comparison of means by Tukey’s method to determine exactly where the significant differences occur.
So, we Reject null hypothesis at 5% level of significance. There is sufficient evi-dence to suggest that the differences occur among the means at 5% level of sig-nificance
.
- Using Durkheim’s theory of anomie (normlessness) as a basis, a sociologist ob-tained the following suicide rates (the number of suicides per 100,000 population), rounded to the nearest whole number, for five high-anomie, five moderate-anomie, and five low-anomie metropolitan areas (anomie was indicated by the extent to which newcomers and transients were present in the population):
| High | Moderate | Low | |
| 19 | 15 | 8 | |
| 17 | 20 | 10 | |
| 22 | 11 | 11 | |
| 18 | 13 | 7 | |
| 25 | 14 | 8 | |
Test the null hypothesis that high-, moderate-, and low-anomie areas do not differ µwith µrespectµ to suicide rates.
Ho: = =
H1: Not all means are equal
- Psychologists studied the relative efficacy of three different treatment programs— A, B, and C—on illicit drug abuse. The following data represent the number of days of drug abstinence accumulated by 15 patients (5 in each treatment program) for the 3 months after their treatment program ended. Thus, a larger number of days indicates a longer period free of drug use.
| Treatment A | Treatment B | Treatment C | |
| 90 | 81 | 14 | |
| 74 | 90 | 20 | |
| 90 | 90 | 33 | |
| 86 | 90 | 5 | |
| 75 | 85 | 12 | |
- Test the null hypothesis that these drug-treatment programs do not differ in regard to their efficacy.
Ho: µ=0
H1: µ≠0
- Conduct a multiple comparison of means by Tukey’s method to determine exactly where the significant differences occur.
Fail to reject the null hypothesis that these drug-treatment programs do not differ in regard to their efficacy.
- Does a woman’s chance of suffering from postpartum depression vary depending on the number of children she already has? To find out, a researcher collected ran-dom samples from four groups of women: the first group having just given birth to their first child, the second group having just given birth to their second child, and so on. He then rated their amount of postpartum depression on a scale from 1 to 5 (where 5 = most depression). Test the null hypothesis that the chances of develop-ing postpartum depression do not differ with the number of children to which a woman has previously given birth.
| Fourth | ||||
| Second | Child | |||
| First Child | Child | Third Child | ||
| 3 | 3 | 5 | 4 | |
| 2 | 5 | 5 | 3 | |
| 4 | 1 | 3 | 2 | |
| 3 | 3 | 5 | 1 | |
| 2 | 4 | 2 | 5 | |
The chance of developing postpartum depression does not depend on the num-ber of children a woman already had.
- Studies have found that people find symmetrical faces more attractive than faces that are not symmetrical. To test this theory, a psychiatrist selected a random sam-ple of people and showed them pictures of three different faces: a face that is per-fectly symmetrical, a face that is slightly asymmetrical, and a face that is highly asymmetrical. She then asked them to rate the three faces in terms of their attrac-tiveness on a scale from 1 to 7, with 7 being the most attractive.
- Test the null hypothesisµthat µattractivenessµ does not differ withµµ facial sym-metry.Null hypothesis= 1 = 2 = 3 Alternative hypothesis
| Slightly Asymmet- | Highly Asymmet- | ||
| Symmetrical | rical | rical | |
| 7 | 5 | 2 | |
| 6 | 4 | 3 | |
| 7 | 5 | 1 | |
| 5 | 2 | 1 | |
| 6 | 4 | 2 | |
| 6 | 5 | 2 | |
- Conduct a multiple comparison of means by Tukey’s method to determine exactly where the significant differences occur.
Reject the null hypothesis. Hence, it can be concluded that, attractiveness does differ with facial symmetry.
- Political theorist Karl Marx is known for his theory that the working class, to put an end to capitalism and establish a communist society, would eventually rise up and overthrow the upper-class members of society who exploit them. One reason for the capitalist workers’ discontent, according to Marx’s theory, is that these workers take no pride in their work because both the work they do and the products that re-sult belong not to them but to the capitalists they work for. To test this insight, a re-searcher went to a large factory and interviewed people from three groups—the workers, the managers, and the owners—to see if there is a difference among them in terms of how much pride they take in their work.
a. Given the following scores, with higher scores representing more pride in work, test the null hypothesis that pride in work does not differ by class.
µ_1 = µ_2 = µ_3 (pride in work does not differ by class)
µ_i = µ_j (pride in work does differ by class)
| Lower (Workers) | Middle (Manag- | Upper (Owners) |
| ers) | ||
| 1 | 4 | 8 |
| 3 | 7 | 7 |
| 2 | 5 | 6 |
| 5 | 6 | 9 |
| 4 | 8 | 5 |
| 2 | 6 | 6 |
| 3 | 5 | 7 |
Conduct a multiple comparison of means by Tukey’s method to determine exactly where the significant differences occur.
Reject the null hypothesis. Hence it can be concluded that, pride in work does dif-fer by class.
- A psychiatrist wonders if people with panic disorder benefit from one particular type of treatment over any others. She randomly selects patients who have used one of the following treatments: cognitive therapy, behavioral therapy, or medication. She asks them to rate on a scale from 1 to 10 how much the treatment has led to a de-crease in symptoms (with a score of 10 being the greatest reduction in symptoms). Test the null hypothesis that the different treatments for panic disorder did not dif-fer in how much they helped these patients.
| Cognitive Therapy | Behavior Therapy | Medication |
| 4 | 6 | 8 |
| 2 | 3 | 6 |
| 5 | 4 | 5 |
| 3 | 8 | 9 |
| 7 | 6 | 3 |
| 5 | 4 | 4 |
| 3 | 7 | 5 |
The different treatment for a panic disorder did not differ in how much they helped in these patients.
.
- Is there a relationship between a mother’s education level and how long she breastfeeds her child? A curious researcher selects samples of mothers from three different education levels and determines their length of breastfeeding (measured in months).
- Test the null hypothesis that education level has no effect on how long a mother breastfeeds her child.
Since F= 4.601 ≥ 3.885, we reject the null hypothsis
| Less Than High | High School Grad- | |
| School | uate | College Graduate |
| 1.0 | 1.5 | 11.0 |
| 6.5 | 4.0 | 6.5 |
| 4.5 | 3.5 | 4.5 |
| 2.0 | 1.5 | 7.5 |
| 8.5 | 5.0 | 9.0 |
- Conduct a multiple comparison of means by Tukey’s method to determine exactly where the significant differences occur.
At 5% level of significance, there is significant enough evidence to support the dale that the education level has no effect on how long a mother breast feeds her child.
- A marriage counselor notices that first marriages seem to last longer than remar-riages. To see if this is true, she selects samples of divorced couples from first, second, and third marriages and determines the number of years each couple was
married before getting divorced.
- Test the null hypothesis that first, second, and third marriages do not differ by marriage length before divorce.
Ho: µ_1 = µ_2 = µ_3
Ha: at least no differ significantly
| First | Second Marriage | Third Marriage | |
| Marriage | |||
| 8.50 | 7.50 | 2.75 | |
| 9.00 | 4.75 | 4.00 | |
| 6.75 | 3.75 | 1.50 | |
| 8.50 | 6.50 | 3.75 | |
| 9.50 | 5.00 | 3.50 | |
- Conduct a multiple comparison of means by Tukey’s method to determine exactly where the significant differences occur.
The first second and third marriages differ by length before divorce
.
- In recent years, a number of cases of high school teachers having sexual relation-ships with their students have made the national news. Interested in how gender
combinations influence perceptions of impropriety, a social researcher asks 40 re-spondents in a survey of education issues about their reaction to a story of a 16-year-old student who is seduced by a 32-year-old teacher. Assigned at random, one-quarter of the respondents are told about a case involving a male teacher and a male student, one-quarter are given a scenario involving a male teacher and a female student, one-quarter are presented a situation of a female teacher with a male student, and one-quarter are presented a female teacher with a female stu – dent. All respondents are asked to indicate the level of impropriety from 0 to 10, where 0 is not at all improper and 10 as improper as can be imagined. The results are as follows:
| Male Teacher | Female Teacher | |||
| Male Stu- | Female Stu- | Male Stu- | Female Stu- | |
| dent | ||||
| dent | dent | dent | ||
| 10 | 10 | 6 | 5 | |
| 10 | 9 | 7 | 8 | |
| 10 | 9 | 5 | 7 | |
| 9 | 10 | 5 | 9 | |
| 9 | 8 | 2 | 7 | |
| 9 | 6 | 4 | 7 | |
| 10 | 7 | 5 | 5 | |
| 9 | 10 | 7 | 6 | |
| 7 | 9 | 2 | 6 | |
| 9 | 8 | 3 | 10 | |
Using two-way analysis of variance, test gender of teacher, gender of student, and their interaction impact on the level of perceived impropriety surrounding high school teacher–student sexual relationships.
Gender of Teacher has a significant main effect on teacher -student sexual rela-tionship. Interaction gender of male and gender of teacher has also a significant effect on teacher-student sexual relationship.
- How does gender and occupational prestige impact credibility? Graduate students in a public health program are asked to rate the strength of a paper concerning the health risks of childhood obesity. All 30 student raters are given the same paper to evaluate, except that the name and degrees associated with the author have been manipulated by a social researcher. The student raters are randomly assigned to one of six groups, with each group receiving a paper written by a combination of either a male name (“John Forrest”) or female name (“Joan Forrest”) followed by one of three degrees (M.D., R.N., or Ph.D.). The raters are asked to rate the paper from 1 to 5 on clarity, 1 to 5 on strength of argument, and 1 to 5 on thoroughness. The total rating scores (the sum of the three subscores) are given as follows for each student rater in each of the six groups.
| John Forrest | Joan Forrest | |||||
| M.D. | R.N. | Ph.D. | M.D. | R.N. | Ph.D. | |
| 12 | 10 | 10 | 15 | 11 | 11 | |
| 15 | 11 | 8 | 10 | 8 | 11 | |
| 13 | 7 | 13 | 12 | 9 | 12 | |
| 15 | 8 | 12 | 14 | 11 | 8 | |
| 14 | 8 | 9 | 12 | 7 | 8 | |
- Plot the means for the six groups on a chart with degree on the horizontal axis, mean rating on the vertical axis, and separate lines for each gender.
- Using two-way analysis of variance, test if gender of author, author’s de-gree, and their interaction impact on the ratings.
There is a name difference in the total scores.There is no name difference in the total scores. There is a degree difference in the total scores.There is no degree difference in the total scores. There is a name by degree interaction in the total scores.There is no name by degree interaction in the total scores.
- A clinical researcher wants to determine if antidepressants should be used in con-junction with therapy to address post-traumatic stress disorder (PTSD) among re-turning veterans. She designs an experiment with 16 volunteers who had been dis-charged from the military and diagnosed as suffering from PTSD. After a period of 1 year either in therapy or not and either on antidepressants or not, the researcher measures their PTSD symptoms on a scale ranging from 1 (low) to 15 (high). Us-ing a two-way ANOVA, test the null hypothesis that therapy and antidepressants have no effect, either alone or in combination, on PTSD symptoms.
No Antidepressants Antidepressants
| No Therapy | Therapy | No Therapy | Therapy | |
| 9 | 9 | 10 | 7 | |
| 10 | 10 | 11 | 6 | |
| 8 | 14 | 7 | 8 | |
| 13 | 9 | 8 | 11 | |
Reject Ho if F > 4.747225. Since 0.05 < 4.747225, we fail to reject the null hypothesis. Therefore, we cannot conclude that there is a main effect of Therapy. Since 2.67 <
4.747225, we fail to reject the null hypothesis. Therefore, we cannot conclude that there is a main effect of Antidepressants. Since 0.49 < 4.747225, we fail to reject the null hy-pothesis. Therefore, we cannot conclude that there is an interaction effect
