Module 11 Assignment - (Matched Pairs)
[Refer to the Module 11a slides for a practice example]
We randomly select 10 individuals from a large group who has participated in an SAT-Math tutorial. We would like to find out if there is good evidence that the tutorial improves average scores on the SAT-M test. Each individual's baseline score and score after the tutorial is recorded below (along with the difference between the baseline and the after tutorial test). We can assume that the distribution of difference is relatively normal.
| Individual # | SAT-M Baseline | SAT-M (after tutorial) | Difference |
| 1 | 680 | 690 | 10 |
| 2 | 540 | 560 | 20 |
| 3 | 590 | 600 | 10 |
| 4 | 620 | 620 | 0 |
| 5 | 630 | 600 | -30 |
| 6 | 660 | 670 | 10 |
| 7 | 490 | 500 | 10 |
| 8 | 510 | 500 | -10 |
| 9 | 700 | 710 | 10 |
| 10 | 420 | 443 | 23 |
The average difference from the sample is 5.3 and the sample standard deviation is 15.4
A researcher hopes to find evidence that the tutorial increases overall SAT-M scores.
1. What are the null and alternative hypothesis statements for this problem?
2. Using the equation below, calculate the resulting t-statistic (show your work and/or describe the process)
3. Report the degrees of freedom and the critical value for an alpha level of .05 (see table below)
4. Can we reject the null hypothesis? Why or why not?
