Question 1178999
This is a two sample t test.
Assume normally distributed, and that sigma may be approximated by s.  Each athlete is his or her own control.
Ho: difference=0
Ha: difference NE 0
alpha 0.10 p{reject Ho|Ho true}
test paired t 0.95, df=7
critical value |t|>1.895
test is t=(d-0)/s/sqrt(8)
mean is 3.5
s=4.24
t=3.5*sqrt(8)/4.24=2.33
reject Ho
there is evidence to support a difference in favor of the new shoes.
p-value is 0.026