According to a genetic model, three mutually exclusive characteristics A, B, C are present with probabilities:
P(A) = 0.1, P(B) = 0.2, P(C) = 0.7
In a random sample of size 100, A happens to appear 15 times, B 23 times, and C 62 times. Can we accept this model with confidence level [Alpha] = .05?
I am new to this site. If there is anything wrong with my question or the way I have asked it, please tell me so that I can fix it. This is an old qual problem from my department.
My guess is that I need to do some sort of hypothesis test or confidence interval, but I am unable to see how to do this with the three variables. I would think to do three separate Likelihood Ratio Tests but I do not know how to set this up.
I would make a Chi-Square-Test.
$T=\sum _{i=1}^3 \frac{(t_f-e_f)^2}{t_f}=\frac{(10-15)^2}{10}+\ldots$
$t_f$=theoretical frequency, $e_f$=empirical frequency
df=3-0-1=2
$H_0: \pi_1=0.1,\pi_2=0.2,\pi_3=0.7$
If $T<\chi ^2_{1-\alpha, df}$, then $H_0$ will be not rejected.
greetings,
calculus