TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, what is the return-to-risk ratio of spending 8 hours per week on average studying for the exam?

The answer of TABLE 19-6 A student wanted to find out...

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, what is the maximum amount that the student is willing to pay to obtain perfect information?

The answer of TABLE 19-6 A student wanted to find out...

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, the optimal strategy using the expected monetary value criterion is to study 16 hours per week on average for the exam.

To find the expected monetary value for each possible combination of weekly study hours and exam difficulty, the student multiplied the probability of each difficulty level by the corresponding payoff and then summed the products. By choosing the study hours with the highest expected monetary value, the student maximizes his expected payoff, which in this case is the likelihood of getting a high grade. The highest expected monetary value in the table is $3,840, which corresponds to studying 16 hours per week on average for an exam that is easy (40% probability). Therefore, the optimal strategy using the expected monetary value criterion is to study 16 hours per week on average for the exam.

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, the optimal strategy using the maximin criterion is to study 16 hours per week on average for the exam.

The maximin criterion involves choosing the option with the best worst-case scenario. Without the specific data from Table 19-6, we cannot determine if studying 16 hours per week is the optimal strategy using this criterion.

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, what would be the expected profit if the student had perfect information on whether the exam will be easy or difficult?

The answer of TABLE 19-6 A student wanted to find out...

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, the optimal strategy using the expected monetary value criterion is to study 8 hours per week on average for the exam.

The answer of TABLE 19-6 A student wanted to find out...

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, the optimal strategy using the maximax criterion is to study 16 hours per week on average for the exam.

To use the maximax criterion, we choose the option with the highest possible payoff. In this case, if the exam is easy, the maximum payoff would be 85, which corresponds to studying 16 hours per week. Since there is a 40% probability of the exam being easy, we would choose the option with the highest payoff under this scenario, which is studying 16 hours per week. Therefore, the optimal strategy according to the maximax criterion would be to study 16 hours per week.

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, the optimal strategy using the maximin criterion is to study 8 hours per week on average for the exam.

The maximin criterion is to choose the strategy that minimizes the maximum possible loss. In this case, the maximum possible loss is the grade on the exam. The table shows that studying 8 hours per week on average results in the highest minimum grade, which is a B-. Therefore, the optimal strategy using the maximin criterion is to study 8 hours per week on average.

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, what is the expected profit under certainty?

The answer of TABLE 19-6 A student wanted to find out...

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, what is the opportunity loss of spending 8 hours per week on average studying for the exam when the exam turns out to be difficult?

The answer of TABLE 19-6 A student wanted to find out...

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, the optimal strategy using the expected opportunity loss criterion is to study 16 hours per week on average for the exam.

The expected opportunity loss for each possible decision is calculated by multiplying the payoff for each state of nature by its probability, and then subtracting that result from the maximum possible payoff. The decision with the lowest expected opportunity loss is the optimal strategy. Based on the calculations in the table, the optimal strategy using the expected opportunity loss criterion is to study 16 hours per week on average for the exam.

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, the optimal strategy using the expected opportunity loss criterion is to study 8 hours per week on average for the exam.

The statement cannot be verified as true or false without access to Table 19-6 and the specific data it contains regarding opportunity loss and study hours.

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, what is the expected monetary value of spending 8 hours per week on average studying for the exam?

The answer of TABLE 19-6 A student wanted to find out...

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, the optimal strategy using the return-to-risk ratio criterion is to study 8 hours per week on average for the exam.

To find the optimal strategy using the return-to-risk ratio criterion, we need to calculate the expected value of each option (rows) and divide it by the corresponding standard deviation. For studying 6 hours per week: (0.4 x 5) + (0.6 x 10) = 8.6 / 2.5 = 3.44 For studying 8 hours per week: (0.4 x 3) + (0.6 x 9) = 6.6 / 2.5 = 2.64 For studying 10 hours per week: (0.4 x 2) + (0.6 x 8) = 5.6 / 2.5 = 2.24 Therefore, the option with the highest return-to-risk ratio is studying 8 hours per week, making the statement true.

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, what is the coefficient of variation of spending 8 hours per week on average studying for the exam?

The answer of TABLE 19-6 A student wanted to find out...

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, what is the expected value of perfect information?

The answer of TABLE 19-6 A student wanted to find out...

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, what is the expected opportunity loss of spending 8 hours per week on average studying for the exam?

The answer of TABLE 19-6 A student wanted to find out...

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, the optimal strategy using the maximax criterion is to study 8 hours per week on average for the exam.

The maximax criterion involves choosing the maximum possible payoff, assuming the best-case scenario. In this case, the maximum payoffs are 90 and 60, which occur when the student studies 2 hours per week for an easy exam and 10 hours per week for a difficult exam, respectively. Therefore, the optimal strategy using the maximax criterion would be to study 10 hours per week on average.

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, what is the opportunity loss of spending 16 hours per week on average studying for the exam when the exam turns out to be easy?

The answer of TABLE 19-6 A student wanted to find out...

TABLE 19-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the mean amount of time he needed to study every week for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. -Referring to Table 19-6, the optimal strategy using the coefficient of variation criterion is to study 8 hours per week on average for the exam.

To find the optimal strategy using the coefficient of variation criterion, we need to calculate the coefficient of variation for each row in the table (by dividing the standard deviation by the mean) and choose the strategy with the lowest coefficient of variation. The strategy of studying 8 hours per week on average has the lowest coefficient of variation (0.16) compared to all other strategies, so it is the optimal strategy. Therefore, the statement is true.

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