A statistics professor was interested in determining if working collaboratively helped students to identify the appropriate statistics test. To find out, she had 1,000 statistics students complete a pretest that included six scenarios for which students had to identify the appropriate statistics test. After the pretest, the instructor had students work in collaborative groups using a statistics decision aid. One week later, she gave the same students a posttest that was similar to the pretest. Test scores were used to measure performance. The results of the paired samples t test were significant at the .001 level with an effect size of .04. Can the statistics professor conclude that working collaboratively is effective? Explain.

To assist you with answering the above questions, consider (and answer) the following:

a. What is the role of significance and sample size in interpreting these results?

b. What is the role of power when a result is not statistically significant?

c. What is the role of power when a result is statistically significant?

d. What factors will increase power?

e. What are the disadvantages of increasing power by (1)using a more lenient significance level or (2) using a one-tailed rather than a two-tailed test?

f. What is the problem with the research design used for this study? How would you improve upon this research design?