## Multinomial Experiement or "Goodness of fit" tests

Hi,

I am trying to figure out these multinomial experiments. The biggest problem I have with them is figuring out the expected values when they are not given (which is always the case ). The two formulas I have been trying to use are

E= np (sum of all observed multiplied by each probability) [but only if they are all not equal]

E= n/k (sum of all observed divided by the number of catagories) [only if they are all assumed equal]

1. Based on a theory, a researcher predicts eye color for first-born children. The actual counts of eye colors for the predicted children are as follows: 132 brown eyes, 17 blue eyes, and 0 green eyes. The researcher predicted for a number of couples that 87% of the offspring would have brown eyes, 8% would have blue eyes, and 5% would have green eyes. Use a 0.05 significance level to test the claim that the actual frequencies correspond to the predicted distributions.

In this problem, do we assume they want to test that the values are non-equal? I guess my real question is: how do we determine whether or not they want the values to be equal or not (if they don't tell in the problem), does it have something to do with the "frequencies correspond to the predicted distributions"?

Thank you very much for any insight!