A company manufactures and markets a traditional type of disposable coffee cup that is used in many fast food restaurants. The company has created a new cup that it believes insulates better than the traditional cup. To investigate whether the new cup insulates better, the company plans to conduct a study. In the study, a random sample of cups for each of the two types will be selected. In each sample, each cup will be filled with the same amount of coffee that has been heated to 150 degrees Fahrenheit (ºF). The amount of time (in minutes) it takes for the coffee to cool to 100º F will be measured for each cup.
The hypotheses that the company will test are shown below, where µN is the true mean time it takes coffee to cool from 150º F to 100º F in the new cup and µT is the true mean time it takes coffee to cool from 150º F to 100º F in the traditional cup.
H0: μN = μT
Ha: μN > μT
Describe a Type II error in the context of the study.
