Final answer:
The statement about expected value analysis in the question is false. Expected value analysis consists of multiplying each outcome by its probability and summing the products to get the mean outcome over many trials.
Step-by-step explanation:
The statement provided in the question suggests that expected value analysis involves subtracting the actual projected outcome from the historical outcome, multiplying by its probability, and then summing these totals. However, this understanding of expected value analysis is false.
Expected value analysis actually consists of multiplying each possible outcome by its corresponding probability and then summing all of these products together to get a single number, which represents the average outcome if the experiment were to be repeated many times.
In statistics, the expected value, or mean, of a discrete random variable is a measure of the center of the distribution of the variable. Essentially, the expected value is the long-term average or mean that results from an experiment after a large number of trials. Importantly, the expected values used in a goodness-of-fit test are the theoretical outcomes predicted by the null hypothesis, not historical outcomes.
Here is a practical example to demonstrate how expected value is calculated: If we have a random variable X representing the roll of a fair six-sided die, the expected value E(X) = (1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6)) = 3.5. This is the average value we would expect over a large number of die rolls.