Educational Analytics Inc. claims to have developed a new math curriculum that will increase performance on tests of student comprehension of math concepts. The existing baseline for all kids tested in the United States on the Math Concept Comprehension Test was a mean score of 100. The new curriculum was tested on a sample of 400 kids, and the mean for the sample was 102 with an SD of 10.

a) Calculate t showing at least one intermediate step.

b) Which number in the problem represents mu?

c) Looking up t in the t-chart, we find that our calculated t far exceeds the critical value for an alpha level of .05. In other words, p < .05. (You can take my word for this, or you can look at the t-chart for yourself; it is in Appendix B.) Now write a short letter to Educational Analytics Inc. stating your decision regarding whether or not to adopt the new curriculum and providing a short explanation (two to three sentences) in wording that the shareholders will be able to understand.

d) New and different story: Let’s say that we had tested the new curriculum with a sample of 400 kids (same sample size as in previous version), and it turned out that the sample mean was 101 and that the sample SD was 20. Do these results, when compared to the results given in the previous story, make it “more” or “less” likely that we would decide to adopt the new curriculum. A one-word answer is fine!

e) What if we were to vary the calculations to match the following information?

i) New mean = 104, n = 64, s = 5.

ii) New mean = 101, n = 400, s = 5.

iii) New mean = 101, n = 36, s = 10.

f) In general, can you state which makes it more likely that the result is statistically significant?

i) Large or small gap between old and new means?

ii) Large or small sample size?

iii) Large or small standard deviation?

Bonus: Think about the formula for t, and point out how each quantity contributes to a large or small t.