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ICE Princess25 [194]
3 years ago
14

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 for 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 99% two-sided confidence interval for the mean peak power after training. Assume population is approximately normally distributed.
Mathematics
1 answer:
Hatshy [7]3 years ago
5 0

Answer:

The 99% confidence interval for the mean peak power after training is [299.4, 330.6]

299.4\leq\mu\leq 330.6

Step-by-step explanation:

We have to construct a 99% confidence interval for the mean.

A sample of n=7 males is taken. We know the sample mean = 315 watts and the sample standard deviation = 16 watts.

For a 99% confidence interval, the value of z is z=2.58.

We can calculate the confidence interval as:

M-z\sigma/\sqrt{n}\leq\mu\leq M+z\sigma/\sqrt{n}\\\\315-2.58*16/\sqrt{7}\leq\mu\leq 315+2.58*16/\sqrt{7}\\\\315-15.6\leq \mu\leq 315+15.6\\\\299.4\leq\mu\leq 330.6

The 99% confidence interval for the mean peak power after training is [299.4, 330.6]

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