Question

A social researcher decides to test whether an individual's age and their opinion on the legalization of marijuana are independent. The researcher randomly interviews 1500 individuals to determine their opinion regarding the legalization of marijuana. The results are given in the following contingency table. OPINION ON THE LEGALIZATION OF MARIJUANA AGES FOR AGAINST UNDECIDED Row Totals 17 - 27 a) 170 b) 100 c) 130 400 28 - 38 d) 155 e) 70 f) 125 350 39 - 49 g) 130 h) 100 i) 120 350 50 & Over j) 145 k) 130 l) 125 400 Column Totals 600 400 500 1500 The expected value for cell k is: Question 21 options: a) 116.67 b) 140 c) 106.67 d) 133.33 e) 130

Answer 1

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:

1. Identify the row total for “50 & Over” which is 400.
2. Identify the column total for “Against” which is 400.
3. Identify the grand total, which is 1500.
4. Calculate the expected value using the formula: (Row Total × Column Total) / Grand Total.
5. 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.