Researchers believe that skipping breakfast can lead to a greater prevalence of fatigue in midmorning. In a random sample of 200 people who skipped breakfast, 82 reported that they experienced mid- morning fatigue; in an independent sample of 300 people who ate breakfast, 87 reported experiencing midmorning fatigue. (a) Let pi be the proportion of people who skip breakfast and experience midmorning fatigue, and let p, be the proportion of people who eat breakfast and experience midmorning fatigue. State the appropriate null and alternative hypotheses that can be used to test the researcher's suspicions. (b) Calculate the value of the test statistic; make sure to show all intermediate calculations to ensure the potential of receiving partial credit. (c) Calculate the p-value associated with this sample, and shade a region on an appropriate curve which represents the p-value. (d) What conclusions would you make if using a significance level of a = 0.01?

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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.