Final answer:
The expected value for cell k in the given contingency table is calculated by multiplying the row total for '50 & Over' with the column total for 'Against' and then dividing by the grand total, resulting in a value of 106.67.
Step-by-step explanation:
The question is asking to calculate the expected value for cell k in a contingency table based on the opinions of individuals of various age groups regarding the legalization of marijuana. The expected value for a cell in a contingency table is calculated by multiplying the row total by the column total and then dividing by the grand total.
To find the expected value for cell k:
- Identify the row total for “50 & Over” which is 400.
- Identify the column total for “Against” which is 400.
- Identify the grand total, which is 1500.
- Calculate the expected value using the formula: (Row Total × Column Total) / Grand Total.
- Perform the calculation: (400 × 400) / 1500 = 160000 / 1500 = 106.67.
Therefore, the expected value for cell k is 106.67.
Expected payoff under certainty refers to the expected outcome when the decision-maker has complete information and knows the probabilities associated with each possible outcome. In this case, the decision-maker can calculate the expected monetary value by multiplying each possible outcome by its probability and summing them up. Option c is the correct answer.
On the other hand, expected value of the best act without certainty considers a situation where the decision-maker does not have complete information and must make a decision based on probabilities. The decision-maker selects the best act based on the expected value, which is calculated by multiplying the payoff for each possible outcome by its probability and summing them up.