Question

Please do all parts! Do not use statistics software. I want to see the formulas.

study of the effect of caffeine on muscle metabolism used 24 male volunteers who each underwent arm exercise tests. 12 of the men were randomly selected to take a capsule containing pure caffeine one hour before the test. The other men received a placebo capsule. During each exercise the subject's respiratory exchange ratio (RER) was measured. (RER is the ratio of CO2 produced to O2 consumed and is an indicator of whether energy is being obtained from carbohydrates or fats). The question of interest to the experimenter was whether, on average, caffeine changes RER. Data is in:

Placebo	Caffeine
105	96
119	99
100	94
97	89
96	96
101	93
94	88
95	105
98	88
95	90
103	97
102	92

a. Construct a hypothesis test that detect whether there is difference in RER between two groups at .05 significant level (show steps)

b. Construct a hypothesis test that detect whether Caffeine reduces RER compared to placebo at .05 significant level (show steps)

Answer 1

Conclusion : Based on given data we reject null hypothesis so that we can conclude that we have sufficient evidence to support our claim that there is significant difference in average reading of RER after consumption of Placebo and Caffeine at 5% level of significance

b).

Conclusion : Based on given data we reject null hypothesis sk we can conclude that we have sufficient evidence to support our claim that Caffeine reduced RER compare to placebo at 5% level of significance