Mathematics

A company has developed educational software whose purpose is to improve math skills among third graders. A school has agreed to let the company test the software on a class of students. The students are given a math test and their scores are recorded. Then the students work through the software and they are given a similar exam again.

1) What is the null hypothesis that best addresses the question of whether or not the software improves math skills? What is the alternative hypothesis?
2) Describe how you would carry out the test. Be specific about the formula(s) you would employ.
3) Define Type I error. If the company obtains results that lead it to reject the null hypothesis, can we be certain that the conclusion is correct?
4) The company decides to test for differences in performance across genders. To do so, they run a regression and obtain the following results:

Predicted Change in Score=3+.25Female
R2=.7
Female is a variable whose value is one for females and zero for males. The t-statistic on the constant is 10 and the t-statistic on the coefficient for female is .9. The company elects to use a 5% level of significance. The class is very large, in excess of 30 students.
a) Calculate the expected change in the student’s test score for males and females. Are these results significant? Summarize your conclusion.
b) Define R2. Is this R2 acceptable?
5) The test is only meaningful to the company if the results can be generalized to the larger population. What is the population? List some reasons that the test may not be generalizable.