Homework Problems. b) Is this an experimental or a nonexperimental design? Why?

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1 Homework Problems Assignment 1 (25 points) Due about one week after Module 1 has been covered in class (5 points) A new drug for attention deficit disorders (ADD) in adults is being investigated. A random sample of 32 participants was obtained from a volunteer list of about 4,000 adults who have been diagnosed with ADD. The 32 participants were randomized into 4 groups of equal size with each group receiving 5, 10, 20, or 40 mg of the new drug. After 30 days of drug therapy, all 32 participants were measured on an ADD checklist (scored on a 0 to 78 scale with larger values representing higher levels of ADD symptoms). The sample data are shown below. Group 1 ( 5 mg): Group 2 (10 mg): Group 3 (20 mg): Group 4 (40 mg): b) Is this an experimental or a nonexperimental design? Why? c) What is the response variable and what is the predictor variable in this study? d) Is x fixed or random? Why? e) Examine the scatterplot of the sample data. Are there any obvious outliers or indications of nonlinearity? f) Compute a 95% confidence interval for β 1 and interpret the results. g) The researcher plans to replicate this study in a population of high school students with dosages of 5, 25, and 45 mg (σ x 2 = 266.7). How many students should be sampled to obtain a 95% confidence interval for β 1 that has a width of about 0.2? Use the MS E from this study as the planning value of the within-group error variance. h) Compute the residual skewness and kurtosis (or excess kurtosis) and report the values (Note: SPSS computes excess kurtosis and R computes kurtosis). 1

2 1-2. (5 points) A published report found that young children vary considerably in their estimation of how much breakfast cereal represents one serving. A researcher suspects that some of this variability might be predicted by how much cereal the students are accustomed to eating at home. One hundred 1 st and 2 nd grade students were randomly selected from the approximately 1,200 1 st and 2 nd grade students who attend Los Angeles elementary schools. All students participate in a parent-student conference each year. After the required conference, the 100 randomly selected students were then told that they had been randomly selected to participant in a research study. They were given a normalsize bowl and asked to fill it with cereal equivalent to one serving. In a different room, the student s parent was asked to perform the same task. The amount of cereal (in ounces) was recorded for the 100 student-parent pairs. The HW1-2.sav file contains the sample data. b) Is this an experimental or a nonexperimental design? c) What is the response variable and what is the predictor variable in this study? d) Is x fixed or random? e) Examine the scatterplot of the sample data. Are there any obvious outliers or indications of nonlinearity? f) Compute a 95% confidence interval for β 1 (parent score as the predictor variable) and interpret the results. g) Compute a 95% confidence interval for ρ yx. Compute a 95% confidence interval for ρ 2 yx. Interpret the results for both confidence intervals. h) Use the 95% confidence interval for ρ yx to test H 0: ρ yx =.3 for α =.05. What is your decision? i) The researcher plans to replicate this study in Alabama. How many students are needed to obtain a 95% confidence interval for ρ yx that has a width of about 0.25? Use the lower 95% limit of ρ yx from this study as your planning value for ρ yx. j) Compute the skewness and kurtosis (or excess kurtosis) for the parent and child scores and report the values. 2

3 1-3. (5 points) A cognitive psychologist developed a new spatial ability test and wants to assess its correlation with performance in a geometry course (criterion validity evidence) and determine if the correlation is similar for males and females. Random samples of 200 males and 200 females were obtained from a University of Iowa database of 10,500 male undergraduate students and 11,400 female undergraduate students. The sample correlation was.886 for the male students and.802 for the female students. a) Describe the two study populations. b) Compute a 95% confidence interval for the difference in population correlations. Interpret the result. c) Use Equation 1.31 (with n = 400 and w 0 =.116) to determine how many additional students should be sampled to obtain a 95% confidence interval for the difference in population correlations that will have a width of (5 points) Three different studies estimated the correlation between employee ratings of their supervisors leadership skills and the level of trust they had with their supervisor. All three studies sampled employees who worked in human resource departments. The study population sizes were about 4,000, 7,000, and 2,000 in studies 1 to 3, respectively. The estimated correlations and the sample sizes are given below Study ρ yx n a) Compute a 95% confidence interval for the average correlation for the three study populations. Interpret the result (5 points) Make up a hypothetical but realistic study from your field of interest in which a test or a confidence interval for a population slope or a population Pearson correlation would provide interesting information. Make up hypothetical but realistic data for your response and predictor variables. Analyze the data using SPSS or R. Write a brief description of your hypothetical study that includes a description of your study population, the response and predictor variables, and an interpretation of the results. Attach the SPSS or R output to your report. 3

4 Assignment 2 (25 points) Due about one week after Module 2 has been covered in class (5 points) A random sample of 12 students was taken from a list of th grade students. Each of the 12 students was asked to describe all of the television shows typically watched each week. From this information, the researcher approximated the number of hours watched per week for each student. Each student also completed a mental ability test as part of a group activity that involved other classmates who were not part of the study. The researcher was given permission to access a standardized reading test score for each of the 12 students. The researcher believes that reading scores are negatively related to hours of TV viewing but is concerned that a negative correlation between these two variables might be due to more intelligent students having higher reading scores and also being less interested in TV. The data are given below. Student Reading Score Hrs/week of TV IQ b) What is the control variable? c) Compute a 95% confidence interval for the partial correlation between reading scores and TV hours controlling for IQ and interpret the results. d) The results of this study are potentially interesting but the confidence interval was too wide to report in a scientific publication. The researcher wants to replicate this study and compute a 95% confidence interval that has a width of about How many students should the researcher sample? Use the 95% upper limit of the partial correlation from this study as a planning value (5 points) Twenty male freshman and their fathers were randomly selected from a university orientation for all incoming male students. A trait aggression questionnaire measured on a 0 to 100 scale was given to the sample of 20 male freshman and their fathers. The sons also were asked to estimate the average number hours per day, during their summer break, that they had played any type of violent video game. The sample results are given below where y = son s aggression score, x1 = average hours per day of violent video game playing, and x2 = father s aggression score. Student y x x

5 b) What is the response variable and what are the two predictor variables in this study? c) Compute 95% confidence intervals for the two population slope coefficients and interpret the results. d) Compute a 95% confidence interval for the population squared multiple correlation and interpret this result. e) Compute 95% confidence intervals for semipartial correlation between y and x 1 and y and x 2. Interpret these results. f) Another researcher wants to conduct a similar study using a sample of male community college students and their fathers. The researcher suspects that the population squared correlation is about 0.7 and would like the 95% confidence interval to have a width of.2. How many male freshman should be sampled? 2-3. (5 points) Thirty-six participants were randomly selected from a volunteer pool consisting of about 4,000 undergraduate students. The participants were randomized into one of nine treatment conditions in a 3 3 factorial experiment. The participants each played a computer checker game that was set to a difficulty level of 1 (easiest), 5, or 9 (hardest) and played while 0, 1, or 3 other students watched. The average heart rate during the game was determined for each participant. The sample data are shown below. Difficulty Level Spectators b) What is the response variable and what are the predictor variables in this experiment? c) Compute a 95% confidence interval for the two main effects and the interaction effect. Interpret the results. (Both predictor variables have been centered in the SPSS data file.) d) Use Equation 1.31 to determine the number of participants that should be added to this study to cut each 95% confidence interval width in half (i.e., set w 0/w = 2). 5

6 2-4. (5 points) Stereotype threat is believed to affect members of a stereotyped group who feel extra pressure in situations where their behavior might confirm the negative reputation of their group. A random sample of 20 female participants was obtained from a university database of about 1,200 undergraduate students. The 20 women were randomized into two groups of equal size and were asked to complete a mathematics test. Participants in group 1 were simply told to complete the test. Participants in the group 2 were (falsely) told, Men typically perform better on this particular test than women and the purpose of this study is to help us understand why. The college GPA for each student was used as a covariate. The test scores and GPAs are shown below. Group Variable Scores 1 Test Score GPA Test Score GPA b) What is the response variable and what are the two predictor variables in this experiment? c) Use a GLM with dummy coding to obtain a 95% confidence interval for the difference in population means. A preliminary analysis suggests that the GPA Group interaction is small and the researcher decided to omit this effect from the model. Interpret the results. d) The researcher wants to replicate this study using a larger sample with the goal of obtaining a narrower confidence interval for the population mean difference. How many participants per group are needed to obtain a 95% confidence interval for the population mean difference that has a width of 1.5 using GPA as a covariate. Use the MS E from this study as a planning value of the average within-group residual variance (5 points) Make up a hypothetical but realistic study from your field of interest in which a GLM would provide interesting information. Make up hypothetical but realistic data for your response and predictor variables. Analyze the data using SPSS or R. Write a brief description of your hypothetical study that includes a description of your study population, the response and predictor variables, and an interpretation of the results. Attach the SPSS or R output to your report. 6

7 Assignment 3 (25 points) Due during finals week (6 points) One hundred and twenty students were randomly selected from a directory of about 5,200 freshman at UC Davis. The 120 students were paid to complete a social support questionnaire and a college life satisfaction questionnaire. The following year, both questionnaires were given to 105 of the original 120 students. The HW3-1.sav file contains the sample data with variable names SS1, CLS1, SS2, and CLS2. b) Draw a path diagram with social support at year 1 (SS1) predicting college life satisfaction at year 1 (CLS1) and social support at years 1 and 2 (SS1 and SS2) predicting college life satisfaction at year 2 (CLS2) c) Compute 95% confidence intervals for the three population slope coefficients and interpret the results. 7

8 3-2. (9 points) One hundred and fifty female students were randomly selected from the directories of two San Jose high schools that contained the names and contact information for about 3,100 female students. Each participant was asked to report their mother s years of education and a description of their mother s current job. The researcher assigned a 1 to 15 occupational status score to each job description. Each participant also answered an educational goals questions that the researcher converted into years of education (e.g., complete high school = 12, get a 2-year college degree = 14, etc.). Each participant also completed a 30-item achievement motivation questionnaire that was scored on a 30 to 210 scale. The HW3-2.sav file contains the sample data with variable names motheroc, mothered, AchMot, and EDgoal. b) Draw a path diagram of a path model with mothered and motheroc predicting AchMot and mothered and AchMot predicting EDgoal. The prediction errors for AchMot and EDgoal are assumed to be uncorrelated. c) Compute 95% confidence intervals for the four population slope coefficients for the path model described above and interpret the results. d) Estimate the indirect effects of motheroc and mothered on EDgoal. Compute 95% confidence intervals for these two population indirect effects and interpret the results. e) Estimate the total effect of mothered on EDgoal. Compute a 95% confidence interval for the population total effect and interpret the results (10 points) Answer Module 3 Study Guide Concept Questions 12, 13, and 14. 8

9 Optional Assignment 4 Due during finals week. Option A (5 extra credit points) Reanalyze your data in Assignments 1-5 and 2-5 using a different statistical package. If you analyzed your data using SPSS, then reanalyze the data using SAS or R. If you analyzed your data using R, then reanalyze the data using SAS or SPSS. Option B (10 extra credit points) Reanalyze your data in Assignments 1-5 and 2-5 using two different statistical packages. If you analyzed your data using SPSS, then reanalyze the data using SAS and R. If you analyzed your data using R, then reanalyze the data using SAS and SPSS. 9