Background: After spending this last semester interning for Mayberry City and Sheriff Andy, you have been provided an opportunity to take your analytical skills to the state level. However, before securing the position, you will be asked to answer the below questions and ensure that you are prepared to work as a state research analyst.
1. The state has adopted a new job training program and you are asked to evaluate the effectiveness of the program. Participants were asked to record their hourly rate before a program. Six months following the training program, participants then reported their new hourly rate and you would like to compare the difference. Employing the trainingprogram dataset, compare whether the program was effective toward increasing the hourly rate of participants within the state. (8 Pts.)
a. Based on the available data, what statistical test should you conduct?
b. After conducting your selected test, copy your SPSS output below.
c. Provide at least two ways for knowing if your results are statistically significant.
d. Interpret your results. Would you recommend that your department continue with the program based on the result?
2. The Health Department is worried about post-partum depression in new mothers in the state. To combat post-partum, mothers are encouraged to participate in one of two programs. The first program includes group therapy between new mothers with regular therapy sessions with a licensed counselor. The second program only includes the group therapy between the new mothers. Finally, some new mothers chose not to participate in either program. A random sample of each group is taken and a psychological evaluation is administered six months after the birth of the child. Mothers who did not participate in the program are coded as 0. Mothers who participated in both group therapy and regular counseling are coded as 1. Mothers who participated in only the group therapy are coded as a 2. Using the postpartum dataset, conduct a statistical test to examine if there is a difference between those mothers who participate in one of the programs and those who do not. (10 Pts.)
a. What statistical test should you conduct for this data?
b. Examining the data output, can we assume homogeneity why or why not? If we cannot assume homogeneity (hypothetical) which alternative tests should we use to evaluate the F-test?
c. Running our analysis, what does our F-test Statistic and p-value tell us about the data?
d. Employing a Tukey test are any of our group means significantly different from each other? Use both the p-value and confidence intervals to examine the difference in means. Include your SPSS output below.
e. Include a printout of the Means Plot below.
3. One of the most important early education factors for children is their ability to read. The State Board of Education wants you to analyze the factors which have the greatest influence on a child’s reading progress for schools in Cedar City. To complete this study, you took a random sample of 20 students and measured their age, memory, IQ, and finally their current reading scores. Running multiple linear regression answer the following questions. (12 pts.)
a. Employing SPSS and the child_data dataset run multiple regression analyzing how age, memory, and IQ influence reading scores. Provide your SPSS output of the coefficients below.
b. Interpret each of the unstandardized coefficients in relation to their effect on the dependent variable.
c. Which of the variables are statistically significant and how do you know?
d. Examining the variables which variables have the greatest and least effect on the dependent variable and how do you know?
e. What is multicollinearity and heteroscedasticity and how do they affect regression models?
f. Does this model suffer from multicollinearity? Explain.