Homework assistance for accounting students. Refer to the Journal of Accounting Education (Vol. 25, 2007) study of assisting accounting students with their homework, Exercise 9.30 (p. 545). Recall that 175 accounting students took a pretest on a topic not covered in class and then each was given a homework problem to solve on the same topic. The students were assigned to one of three homework assistance groups. Some students received the completed solution, some were given check figures at various steps of the solution, and some received no help at all. After finishing the homework, the students were all given a posttest on the subject. The dependent variable of interest was the knowledge gain (or test score improvement). These data are saved in the file.
a. Propose a model for the knowledge gain (y) as a function of the qualitative variable, homework assistance group.
b. In terms of the b’s in the model, give an expression for the difference between the mean knowledge gains of students in the “completed solution” and “no help” groups.
c. Fit the model to the data and give the least squares prediction equation.
d. Conduct the global F-test for model utility using = .05. Interpret the results, practically.
e. Show that the results, part d, agree with the conclusions reached in Exercise 9.30.
Exercise 9.30
Homework assistance for accounting students. Refer to the Journal of Accounting Education (Vol. 25, 2007) study of assisting accounting students with their homework, Exercise 8.18 (p. 468). A total of 75 junior-level accounting majors who were enrolled in Intermediate Financial Accounting participated in the experiment. Recall that students took a pretest on a topic not covered in class and then each was given a homework problem to solve on the same topic. A completely randomized design was employed, with students randomly assigned to receive one of three different levels of assistance on the homework: (1) the completed solution, (2) check figures at various steps of the solution, and (3) no help at all. After finishing the homework, each student was given a posttest on the subject. The response variable of interest to the researchers was the knowledge gain (or, test score improvement), measured as the difference between the posttest and pretest scores. The data (simulated from descriptive statistics published in the article) are saved in the accompanying file.
a. Give the null and alternative hypotheses tested in an analysis of variance of the data.
b. Summarize the results of the analysis in an ANOVA table.
c. Interpret the results, practically. Does your conclusion agree with the inferences drawn in Exercise 8.18?
Exercise 8.18
Homework assistance for accounting students. How much assistance should accounting professors provide students for completing homework? Is too much assistance counterproductive? These were some of the questions of interest in a Journal of Accounting Education (Vol. 25, 2007) article. A total of 75 junior-level accounting majors who were enrolled in Intermediate Financial Accounting participated in an experiment. All students took a pretest on a topic not covered in class; then each was given a homework problem to solve on the same topic. However, the students were randomly assigned different levels of assistance on the homework. Some (20 students) were given the completed solution, some (25 students) were given check figures at various steps of the solution, and the rest (30 students) were given no help. After finishing the homework, each student was given a posttest on the subject. One of the variables of interest to the researchers was the knowledge gain (or, test score improvement), measured as the difference between the posttest and pretest scores.
The sample mean knowledge gains for the three groups of students are provided in the table.
a. The researchers theorized that as the level of homework assistance increased, the test score improvement from pretest to posttest would decrease. Do the sample means reported in the table support this theory?
b. What is the problem with using only the sample means to make inferences about the population mean knowledge gains for the three groups of students?
c. The researchers conducted a statistical test of hypothesis to compare the mean knowledge gain of students in the “no solutions” group with the mean knowledge gain of students in the “check figures” group. Based on the theory, part a, set up the null and alternative hypotheses for the test.
d. The observed significance level of the t-test of part c was reported as .8248. Using = .05, interpret this result.
e. The researchers conducted a statistical test of hypothesis to compare the mean knowledge gain of students in the “completed solutions” group with the mean knowledge gain of students in the “check figures” group. Based on the theory, part a, set up the null and alternative hypotheses for the test.
f. The observed significance level of the t-test of part e was reported as .1849. Using = .05, interpret this result.
g. The researchers conducted a statistical test of hypothesis to compare the mean knowledge gain of students in the “no solutions” group with the mean knowledge gain of students in the “completed solutions” group. Based on the theory, part a, set up the null and alternative hypotheses for the test.
h. The observed significance level of the t-test of part g was reported as .2726. Using = .05, interpret this result.