Final answer:
The statement is false; the expectations hypothesis is an economic term unrelated to the expected value in statistics, which is the sum of values weighted by their probabilities. Expected values are used in goodness-of-fit tests to compare with observed data to make decisions about null hypotheses.
Step-by-step explanation:
The statement "According to the expectations hypothesis, the expected value is the sum of the probabilities of all expected events" is false. The expectations hypothesis is related to finance and economic models where it suggests that current long-term interest rates reflect market participants' expectations of future short-term rates. However, when talking about expected value in the context of probability and statistics, it is defined as the sum of all possible values each multiplied by the probability of its occurrence which is represented as E(X) = ΣxP(x), where Σ denotes the summation, x is a value that the random variable can take on, and P(x) is the probability of x occurring.
When applying this to a goodness-of-fit test, the expected values indeed represent what we would expect if the null hypothesis were true. A large discrepancy between observed and expected values could lead to a large test statistic, indicating that the null hypothesis is unlikely. Whereas in quantum mechanics, expectation values represent average measurements expected from a quantum system, which is a different concept altogether.