An article in Medicine and Science in Sports and Exercise \"Maximal Leg-Strength

Question

An article in Medicine and Science in Sports and Exercise "Maximal Leg-Strength Training Improves Cycling Economy in Previously Untrained Men," (2005, Vol. 37 pp. 131-1236) studied cycling performance before and after eight weeks of leg-strength training. Seven previously untrained males performed leg-strength training three days per week tor eight weeks (with four sets of five replications at 85% of one repetition maximum). Peak power during incremental cycling increased to a mean of 315 watts with a standard deviation of 16 watts. Construct a 95% confidence interval for the mean peak power after training.

Explanation / Answer

Since we're not given the standard deviation of the population, but rather of the sample, we must use a T-Interval to calculate the 95% confidence interval as opposed to a Z-Interval. There are 6 degrees of freedom (sample size - 1), so the appropriate t-value for 95% confidence and 6 degrees of freedom is 2.447 (by looking at a table).

The 95% confidence interval can be found by the formula:

315 ± (2.447)/n

Where is the standard deviation of the sample and n is the sample size. This is equivalent to:

315 ± (2.447)(16)/7 = 315 ± 14.80

So the 95% confidence interval for the mean would be (300.2, 329.8)

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