A student in training for an 800 meter event recorded their fastest times for 800 meters during practice sessions in August, September, October, and November. The student wants to know if they are improving. Remember that for times, smaller values are faster times.

 Data Data Date Time (sec) Date Time (sec) 08/23/09 167 10/25/09 163 08/25/09 175 10/28/09 165 08/27/09 166 10/31/09 172 08/30/09 179 11/09/09 163 09/01/09 169 11/15/09 169 09/03/09 159 11/18/09 164 09/09/09 166 11/21/09 159 09/15/09 168 11/24/09 166
1. What is the average time for the runner in August and September?
2. What is the average time for the runner in October and November?
3. Is the runner mathematically faster in October and November?
4. When comparing the means for these two samples, which test should be run:
a paired t-test or independent samples t-test?
5. Determine the two-tailed p-value.
6. Determine the two tailed maximum confidence c that the difference is stat. sig.
7. Write out the null hypothesis in plain English.
8. At a risk of a type I error of 0.05 (alpha = 0.05), would we:
Reject the null hypothesis | OR | Fail to reject the null hypothesis?
9. Is the student statistically significantly faster in October and November than in August and September at a 5% risk of rejecting a true null hyp?
10. Can we be 95% certain the student is stat. sig. faster in October and November?
11. If we go ahead and say the student is faster, what is our risk of being wrong?