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HOMEWORK #1
- A researcher measures job satisfaction among married, single, and divorced employees to determine whether marital status can influence job satisfaction. Based on the following description in APA format, state the value for k, N, and n.
A one-way analysis of variance showed that job satisfaction did not vary by marital status,
F(3, 36) = 1.86, p > 0.05.
k | = | |
N | = | |
n | = |
- The following is an incomplete F-table summarizing the results of a study of the variance of life satisfaction scores among unemployed, retired, part-time, and full-time employees.
Source of Variation | SS | df | MS | F |
Between groups | 16 | |||
Within groups (error) | 36 | |||
Total | 124 |
(a) Complete the F-table. (Round your values for mean squares and F to two decimal places.)
Source of Variation | SS | df | MS | F |
Between groups | 16 | |||
Within groups (error) | 36 | |||
Total | 124 |
(b) Compute omega-squared
(ω^{2}).
(Round your answer to two decimal places.)
ω^{2} =
- Iconic memory is a type of memory that holds visual information for about half a second (0.5 seconds). To demonstrate this type of memory, participants were shown three rows of four letters for 50 milliseconds. They were then asked to recall as many letters as possible, with a 0-, 0.5-, or 1.0-second delay before responding. Researchers hypothesized that longer delays would result in poorer recall. The number of letters correctly recalled is given in the table.
Delay Before Recall | ||
0 | 0.5 | 1 |
12 | 8 | 4 |
7 | 4 | 2 |
8 | 4 | 4 |
10 | 9 | 7 |
5 | 6 | 2 |
12 | 5 | 5 |
(a) Complete the F-table. (Round your values for MS and F to two decimal places.)
Source of Variation | SS | df | MS | F |
Between groups | ||||
Within groups (error) | ||||
Total |
(b) Compute Tukey’s HSD post hoc test and interpret the results. (Assume alpha equal to 0.05. Round your answer to two decimal places.)
The critical value is for each pairwise comparison.
- An educator wants to evaluate four different methods aimed at reducing the time children spend “off task” in the classroom. To test these methods, she implements one method in each of four similar classrooms and records the time spent off task (in minutes) in each classroom. The results are given in the table.
Classroom Method | |||
A | B | C | D |
1 | 4 | 3 | 2 |
5 | 3 | 0 | 5 |
4 | 5 | 4 | 2 |
2 | 0 | 6 | 4 |
2 | 1 | 0 | 1 |
3 | 1 | 6 | 3 |
0 | 4 | 3 | 3 |
1 | 4 | 4 | 4 |
1 | 0 | 5 | 2 |
(a) Complete the F-table. (Round your answers to two decimal places.)
Source of Variation |
SS | df | MS | F |
Between groups |
||||
Within groups (error) |
||||
Total |
- Drakou, Kambitsis, Charachousou, and Tzetzis (2006) tested differences in life satisfaction among sport coaches. They tested differences by gender, age, marital status, and education. The results of each F-test in the following table are similar to the way in which the data were given in their article.
Independent Variables |
Life Satisfaction | |||
M | SD | F | p | |
Gender | 0.68 | 0.409 | ||
Men | 3.99 | 0.51 | ||
Women | 3.94 | 0.49 | ||
Age | 3.04 | 0.029 | ||
20s | 3.85 | 0.42 | ||
30s | 4.03 | 0.52 | ||
40s | 3.97 | 0.57 | ||
50s | 4.02 | 0.50 | ||
Marital status | 12.46 | 0.000 | ||
Single | 3.85 | 0.48 | ||
Married | 4.10 | 0.50 | ||
Divorced | 4.00 | 0.35 | ||
Education | 0.82 | 0.536 | ||
High school | 3.92 | 0.48 | ||
Postsecondary | 3.85 | 0.54 | ||
University degree | 4.00 | 0.51 | ||
Masters | 4.00 | 0.59 |
(a) Which factors were significant at a 0.05 level of significance? (Select all that apply.)
marital statuseducationgenderage
(b) State the number of levels for each factor.
gender | levels | |
age | levels | |
marital status | levels | |
education | levels |
- Using a rating scale, Tekinarslan (2008) measured computer anxiety among university students who use the computer very often, often, sometimes, and seldom. Below are the results of the one-way ANOVA.
Source of Variation | SS | df | MS | F |
Between groups | 1,959.79 | 3 | 653.26 | 21.16* |
Within groups (error) | 3,148.61 | 102 | 30.86 | |
Total | 5,108.41 | 105 |
(a) What are the values for N and k?
N | = | |
k | = |
- A researcher records the following data for each of three groups.
Group A | Group B | Group C |
12 | 12 | 12 |
17 | 11 | 11 |
5 | 7 | 3 |
6 | 5 | 12 |
10 | 15 | 12 |
What is the value of the F-statistic? (Round your answer to two decimal places.)
F =
Explain your answer.
F is the indicated value because the group means are different. There is no variability between groups.F is the indicated value because the group means are the same. There is no variability between groups. F is the indicated value because the groups means are different. There is substantial variability between groups.F is the indicated value because the group means are the same. There is substantial variability between groups.
- A child psychologist treats four children who are afraid of snakes with a behavioral modification procedure called systematic desensitization. In this procedure, children were slowly introduced to a snake over four treatment sessions. Children rated how fearful they are of the snake before the first session (baseline) and following each treatment session. Higher ratings indicated greater fear. The hypothetical data are listed in the table.
Sessions | ||||
Baseline | 1 | 2 | 3 | 4 |
7 | 7 | 5 | 4 | 3 |
7 | 6 | 6 | 4 | 4 |
6 | 6 | 7 | 7 | 3 |
7 | 7 | 5 | 4 | 3 |
(a) Complete the F-table. (Round your value for F to two decimal places.)
Source of Variation |
SS | df | MS | F_{obt} |
Between groups |
||||
Between persons |
||||
Within groups (error) |
||||
Total |
(b) Compute a Bonferroni procedure and interpret the results. (Assume experimentwise alpha equal to 0.05.)
Ratings of fear significantly decreased from baseline to Session 4.Ratings of fear significantly decreased from baseline to Session 3. Ratings of fear also significantly decreased from Session 1 to Session 4. None of the pairwise comparisons are significant.Ratings of fear significantly decreased from baseline to Session 3. Ratings of fear also significantly decreased from baseline to Session 4.Ratings of fear significantly decreased from Session 1 to Session 4. Ratings of fear also significantly decreased from Session 2 to Session 4.
- A study investigated the effects of physical fatigue on the performance of professional tennis players. Researchers measured the number of unforced errors committed by a random sample of 12 professional tennis players during the first three sets of a match. They hypothesized that increased fatigue would be associated with a greater number of errors. The following is an F-table for this hypothetical study using the one-way within-subjects ANOVA.
Source of Variation | SS | df | MS | F_{obt} |
Between groups | 15 | |||
Between persons | 5 | |||
Within groups (error) | 44 | |||
Total |
(a) Complete the F-table.
Source of Variation |
SS | df | MS | F_{obt} |
Between groups |
15 | |||
Between persons |
5 | |||
Within groups (error) |
44 | |||
Total |
Make a decision to retain or reject the null hypothesis. (Assume alpha equal to 0.05.)
Retain the null hypothesis.Reject the null hypothesis.
(b) Estimate effect size using partial omega-squared: ω_{P}^{2}. (Round your answer to two decimal places.)
ω_{P}^{2} =
- Air traffic controllers perform the vital function of regulating the traffic of passenger planes. Frequently, air traffic controllers work long hours with little sleep. Researchers wanted to test their ability to make basic decisions as they become increasingly sleep deprived. To test their abilities, a sample of 6 air traffic controllers is selected and given a decision-making skills test following 12-hour, 24-hour, and 48-hour sleep deprivation. Higher scores indicate better decision-making skills. The table lists the hypothetical results of this study.
Sleep Deprivation | ||
12 Hours | 24 Hours | 48 Hours |
23 | 19 | 18 |
20 | 22 | 22 |
35 | 24 | 22 |
27 | 21 | 14 |
24 | 16 | 17 |
22 | 22 | 16 |
(a) Complete the F-table. (Round your answers to two decimal places.)
Source of Variation |
SS | df | MS | F_{obt} |
Between groups |
||||
Between persons |
||||
Within groups (error) |
||||
Total |
(b) Compute a Bonferroni procedure and interpret the results. (Assume experimentwise alpha equal to 0.05. Select all that apply.)
There is a significant difference in decision making for the 12-hour and 24-hour sleep deprivation conditions.There are no significant differences between any of the groups.There is a significant difference in decision making for the 12-hour and 48-hour sleep deprivation conditions.There is a significant difference in decision making for the 24-hour and 48-hour sleep deprivation conditions.
- Researchers in mental health fields are often interested in evaluating the effectiveness of using food images to enhance positive mood. Adapting a typical design from such studies, suppose we have participants rate their mood change on a standard self-report affect scale after viewing images of “comfort” foods, fruits/vegetables (F/V), and random non-food images (used as a control group). The results are given in the table at right for this hypothetical study.
Images | ||
Control | F/V | Comfort Foods |
0 | 0 | 4 |
0 | 1 | 3 |
1 | 2 | 3 |
3 | 2 | 6 |
0 | 2 | 0 |
(a) Complete the F-table. (Round your answers to two decimal places.)
Source of Variation |
SS | df | MS | F_{obt} |
Between groups |
||||
Between persons |
||||
Within groups (error) |
||||
Total |
(b) Compute a Bonferroni procedure and interpret the results. (Assume experimentwise alpha equal to 0.05. Select all that apply.)
Participants rated a significantly larger mood change after viewing images of comfort foods compared with the mood change after viewing control images.Participants rated a significantly larger mood change after viewing images of comfort foods compared with the mood change after viewing images of fruits/vegetables.Participants rated a significantly larger mood change after viewing images of fruits/vegetables compared with the mood change after viewing control images.There were no significant differences between any of the groups.
- Wilfley and colleagues (2008) tested whether the antiobesity drug sibutramine would be an effective treatment for people with binge eating disorder. They measured the frequency of binge eating every 2 weeks for 24 weeks during treatment. The following table lists a portion of the data similar to results reported by the authors for the frequency of binge eating over the first 8 weeks of the drug treatment.
Frequency of Binge Eating | ||||
Baseline | Week 2 | Week 4 | Week 6 | Week 8 |
4 | 1 | 0 | 0 | 1 |
6 | 4 | 2 | 0 | 0 |
3 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 1 | 1 |
2 | 2 | 1 | 1 | 1 |
5 | 1 | 2 | 2 | 2 |
(a) Complete the F-table. (Round your answers to two decimal places.)
Source of Variation |
SS | df | MS | F_{obt} |
Between groups |
||||
Between persons |
||||
Within groups (error) |
||||
Total |
Make a decision to retain or reject the null hypothesis. (Assume experimentwise alpha equal to 0.05.)
Retain the null hypothesis.Reject the null hypothesis.
(b) Use the Bonferroni procedure to make the post hoc test. In which week do we first see significant differences compared to baseline?
Week 2 is the first week where significant differences from baseline are evident.Week 4 is the first week where significant differences from baseline are evident. Week 6 is the first week where significant differences from baseline are evident.Week 8 is the first week where significant differences from baseline are evident.None of the weeks are significantly different from the baseline.
- An educator evaluates the effects of small, medium, and large class sizes on academic performance among male and female students. Identify each factor and the levels of each factor in this example. (Select all that apply.)
academic performance (three levels: above average, average, below average)class size (two levels: small, large)gender (two levels: male, female)gender (three levels: male, female, trans)class size (three levels: small, medium, large)academic performance (two levels: passing, failing)
- Seasonal affective disorder (SAD) is a type of depression during seasons with less daylight (e.g., winter months). One therapy for SAD is phototherapy, which is increased exposure to light used to improve mood. A researcher tests this therapy by exposing a sample of patients with SAD to different intensities of light (low, medium, high) in a light box, either in the morning or at night (these are the times thought to be most effective for light therapy). All participants rated their mood following this therapy on a scale from 1 (poor mood) to 9 (improved mood). The hypothetical results are given in the following table.
Light Intensity | ||||
Low | Medium | High | ||
Time of Day |
Morning | 5 | 5 | 7 |
6 | 6 | 8 | ||
3 | 4 | 6 | ||
7 | 7 | 9 | ||
5 | 9 | 5 | ||
6 | 8 | 8 | ||
Night | 5 | 6 | 9 | |
8 | 8 | 6 | ||
6 | 7 | 6 | ||
7 | 5 | 8 | ||
4 | 9 | 7 | ||
3 | 8 | 6 |
(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Round your answers to two decimal places. Assume experimentwise alpha equal to 0.05.)
Source of Variation |
SS | df | MS | F |
Time of day | ||||
Intensity | ||||
Time of day × Intensity |
||||
Error | ||||
Total |
State the decision for the main effect of the time of day.
Retain the null hypothesis.Reject the null hypothesis.
State the decision for the main effect of intensity.
Retain the null hypothesis.Reject the null hypothesis.
State the decision for the interaction effect.
Retain the null hypothesis.Reject the null hypothesis.
(b) Compute Tukey’s HSD to analyze the significant main effect.
The critical value is for each pairwise comparison.
Summarize the results for this test using APA format.
- In an effort to promote a new product, a marketing firm asks participants to rate the effectiveness of ads that varied by length (short, long) and by type of technology (static, dynamic, interactive). Higher ratings indicated greater effectiveness.
Source of Variation | SS | df | MS | F |
Length | 10 | |||
Technology | ||||
Length × Technology | 158 | |||
Error | 570 | 114 | ||
Total | 878 |
(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Assume experimentwise alpha equal to 0.05.)
Source of Variation |
SS | df | MS | F |
Length | 10 | |||
Technology | ||||
Length × Technology |
158 | |||
Error | 570 | 114 | ||
Total | 878 |