Directions:
1. The α level for all the significance tests on this exam will be .05.
2. Please use the SPSS data file in the same exam folder for this assignment.
3. No partial credit will be assigned for a correct verbal conclusion supported by incorrect statistics or an incorrect verbal conclusion supported by correct statistics.
4. Please don’t submit all your SPSS outputs to the instructor and expect him to find the relevant statistics for you.
5. Please submit your answers by the designated deadline. An overdue problem will be assigned 0 point.
A researcher intended to investigate if student midterm exam grades on a 0 - 30 scale would differ across weekly tutoring time in hours (i.e., 0, 1, 2, 3, & 4) in an intermediate statistics course. The omnibus research question was formulated as:
Will average midterm exam grades in an intermediate statistics course differ across weekly tutoring time? Or, equivalently, is weekly tutoring time related to midterm exam grade in an intermediate statistics course?
Due to consideration of the fairness issue, the researcher did not randomly assign students to groups of different weekly tutoring time. Instead, students voluntarily chose to receive tutoring in various hours each week. That is, students self-selected themselves into one of the following 5 weekly tutoring hour groups: (1) 0-hour group (Group 1)
(2) 1-hour group (Group 2)
(3) 2-hour group (Group 3)
(4) 3-hour group (Group 4)
(5) 4-hour group (Group 5)
The researcher was interested in the possible trends existing in the relationship between weekly tutoring time and midterm exam grade in an intermediate statistics course. Please conduct the trend analysis with the SPSS using weekly tutoring time as the independent variable and midterm exam grade as the dependent variable, then answer the following questions:
(a) What will be the null hypothesis in the test of the linear trend in the relationship between weekly tutoring time and midterm exam grade in an intermediate statistics course? (3 points)
(b) What will be the null hypothesis in the test of the cubic trend in the relationship between weekly tutoring time and midterm exam grade in an intermediate statistics course? (3 points)
(c) What is your verbal conclusion for the linear trend in the relationship between weekly tutoring time and midterm exam grade in an intermediate statistics course supported by the relevant F test results and the effect size index (η2) in APA style? (3 points)
(d) What is your verbal conclusion for the cubic trend in the relationship between weekly tutoring time and midterm exam grade in an intermediate statistics course supported by the relevant F test results and the effect size index (η2) in APA style? (3 points)