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 
 What is the average time for the runner in August and September?
 What is the average time for the runner in October and November?
 Is the runner mathematically faster in October and November?
 When comparing the means for these two samples, which test should be run:
a paired ttest or independent samples ttest?
 Determine the twotailed pvalue.
 Determine the two tailed maximum confidence c that the difference is stat. sig.
 Write out the null hypothesis in plain English.
 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?
 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?
 Can we be 95% certain the student is stat. sig. faster in October and November?
 If we go ahead and say the student is faster, what is our risk of being wrong?