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Effect of birth control on exercise capacity

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A physiologist wishes to study the effect of birth control pills on exercise capacity. Five female subjects who have never taken the pill have their maximal oxygen uptake measured during a treadmill session. The five subjects then take the pill for a specified length of time and their uptakes are measured again, as given below. Do the data provide sufficient evidence to indicate that the mean maximal oxygen uptake after taking birth control pills is less than the mean uptake before taking the pill? State the null and alternate hypothesis.
Use α = .01.

MAXIMAL OXYGEN UPTAKE
SUBJECT BEFORE AFTER
1 35.0 29.5
2 36.5 33.5
3 36.0 32
4 39.0 36.5
5 37.5 35.0

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The expert uses the hypothesis tests to determine the effects of birth control.

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A physiologist wishes to study the effect of birth control pills on exercise capacity. Five female subjects who have never taken the pill have their maximal oxygen uptake measured during a treadmill session. The five subjects then take the pill for a specified length of time and their uptakes are measured again, as given below. Do the data provide sufficient evidence to indicate that the mean maximal oxygen uptake after taking birth control pills is less ...

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  • MA, Shandong Univ.
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  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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