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5. Munder Difflin makes a type of single-use coffee cup that is used in many fast-casual restaurants. They have created a new cup that they believe keeps coffee warmer than their old cup. To investigate whether the new cup insulates better, Munder Difflin plans to conduct a study. In the study, an SRS of cups for each of the two types will be selected. In each sample, each cup will be filled with the same volume of coffee that has been pre-heated to 160 degrees Fahrenheit (°F). The amount of time (in minutes) it takes for the coffee to cool to 110 °F will be measured for each cup. The hypotheses that the company will test are shown below, where y, is the true mean time it takes coffee to cool from 160 °F to 110 °F in the new cup and p is the true mean time it takes coffee to cool from 160 °F to 110 °F in the older, traditional cup. Hu H: n = M 0 = N H:Hv> a N (a) Describe a Type II error in the context of the study. (b) Munder Difflin is concerned about the probability of a Type II error. Which test procedure, one that uses a significance level of a = 0.10 or one that uses a significance level of a = 0.01, would result in a smaller probability of a Type II error? Explain. (c) The accounting team in Munder Difflin thinks that a 3-minute increase in the time it takes the coffee to cool from 160 °F to 110 °F would be a noticeable improvement to customers. Suppose a paid statistician estimates that the power of the appropriate significance test is 0.85 when the true mean cooling time for the new cups is 3 minutes greater than the true mean cooling time for the older, traditional cups. Interpret the value of 0.85 in the context of the study.