You want to know whether birthdays are equally distributed through all 12 months, so you take a random sample of 149 people and record each person's birth month. what would you use as the expected value for a chi-square goodness-of-fit test of these data?

The answer is approximately 12.417

Step-by-step explanation:

We have:

First, we have that the number of people observed is 149 and the number of months is 12. Since we want to prove that birthdays of 149 persons are equally distributed over the 12 months, then the test should result in an expected value given by:

We are not calculating the value of the chi-square test, because what we want is to find out what is the expected value of applying that test to a uniformly distributed sample.

translate k to n and reflect across the line containing jk.