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?