Answer to Question #226077 in Statistics and Probability for Carrie

Question

Consider a multinomial experiment involving n D 150 trials and k D 4 cells. The observed frequen-

cies resulting from the experiment are shown in the following table, and the null hypothesis to be

tested is as follow:

H0 : p1 D 0:3 p2 D 0:3 p3 D 0:2 p4 D 0:2

Cell 1 2 3 4

Frequency 38 50 38 24

The expected frequencies are

1. 4:5 4:5 3:0 3:0

2. 45 45 30 30

3. 0:3 0:3 0:2 0:2

4. 30 30 45 45

5. 38 50 38 24

Answer 1

Expected frequencies: $150*0.3=45,\;150*0.3=45,\;150*0.2=30,\;150*0.2=30.$

Var. 2. 45 45 30 30.