We learned that when there is no relationship between two categorical variables

Question

We learned that when there is no relationship between two categorical variables in a population, a "statistically significant" relationship will appear in 5% of the samples from that population, over the long run. Suppose that two researchers independently conduct studies to see whether there is a relationship between drinking coffee (regularly, sometimes, never) and having migraine headaches (frequently, occasionally, never). a. If there really is no relationship in the population, what is the probability that the first researcher finds a statistically significant relationship? b. If there really is no relationship in the population, what is the probability that both researchers find a statistically significant relationship?

Explanation / Answer

let S shows the event that person finds a statistical signifcant relationship. So

P(S) = 0.05

a)

The probability that first person finds a statistical signficant relationship and second person not is

P(first person finds a statistical signficant relationship) = P(S)(1-P(S) = 0.05 * (1-0.05) = 0.0475

b)

Since reseachers are independent so the probability that both reseachers find a statisticalli signficant relationship is

P(both persons find a statistical signficant relationship) = 0.05 * 0.05 = 0.0025

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