Without Breathe-Right 3326 +/- 520 With Breathe-Right 3367 +/- 615 Difference 41.4 +/- 438.3There are many variables that may affect VO2 Max besides whether the "Breathe-Right" nasal strips were worn or not. However, most of these variables (such as age, cardiovascular fitness, etc.) are controlled for by having the same athlete tested twice. Each measurement without the strip is matched to a corresponding measurement on the same individual with the strip. The sixteen individual differences in VO2 Max consist of a single sample of differences.
To test the hypothesis that the nasal strips improve VO2 Max, the test statistic is
t = (41.4 - 0) / (438.3 / sqrt{16}) = 0.38In other words, the observed difference in sample means is 0.38 estimated standard errors above the mean, a value that is easily attributable to chance variation.
A one-sided p-value is 0.35. Since we expect to see a result this extreme 35% of the time when the null hypothesis is true (more than once every three experiments), we are not surprised that it occured. Hence, the data is consistent with the hypothesis that "Breathe-Right" nasal strips have no effect on VO2 Max.
Bret Larget, larget@mathcs.duq.edu