A study of the effect of caffeine on muscle metabolism used eighteen male volunteers who each underwent arm exercise tests. Nine 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). Does the data provide evidence that caffeine does, on average, reduce RER?       Placebo Caffeine   104 96   119 100   100 94   97 89   98 96   103 93   94 89   95 105   98 88 Mean 100.89 94.44 Variance 57.11 31.28

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.