Geneticists say that the color of Italian squash should follow the $12:3:1$ ratio. A group of researchers collects the following information: White 155, yellow 40 and green 10. Are these data consistent with the hypothesis of the geneticists?
I have to perform a chi-square test, but I need the expected frequencies which are obtained with the following formula
$e_i=nπ_i $ where $n$ is the sample size and $π_i$ is the assumed proportions
What I don't understand is how to occupy $12:3:1$, is 12% or $\frac{2}{3}$ or $\frac{\frac{2}{3}}{1}$ ?
The total number of observations is $n = 155 + 40 + 10 = 205$. The theoretical or hypothesized proportions are $\pi_1 = 12/16$ white, $\pi_2 = 3/16$ yellow, and $\pi_3 = 1/16$ green; hence the expected frequency of white is $205(12/16) = 153.75$, and so forth.