1. Do these data provide sufficient evidence for a real relationship in the population? Test at the .05 level, two tails. Use Pearson Correlation

Question

X Y
8 0
6 1
4 4
3 6
4 6
5 1

2. To test the effectiveness of a new studying strategy, a psychologist randomly divides a sample of 8 students into two groups, with n=4 in each group. The students in one group receive training in the new studying strategy. Then all students are given 30 minutes to study a chapter from a history textbook before they take a quiz on the chapter. The quiz scores for the two groups are as follows:

Training:6,13,12,9
No Training : 1,6,6,3

a. Perform a t-test to answer the research question: Is the new studying strategy effective? (In other words, whether there is difference in student scores between the two groups.) Use an alpha of .05.
b. Convert these data into a form suitable for the point-biserial correlation. (use X=1 for training, X=0 for no training, and the quiz scores for Y). Calculate the point-biserial correlation, r, for these data
c. Test if the point-biserial correlation, r, is different from zero using an alpha of .05.
d. Calculate the squared correlation, r2. What does this number mean
e. What statement can be made regarding the results of the independent sample t-test comparing two group means and the results t-test of whether the point-biserial correlation is different from zero?