Question

You are conducting a multinomial Chi-Square Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:

HoHo : pA=0.1; pB=0.5; pC=0.1;  pD=0.3

Complete the table. Report all answers accurate to three decimal places.

Category	Observed Frequency	Expected Frequency
A	17
B	25
C	6
D	16

What is the chi-square test-statistic for this data?
χ2=

What is the P-Value?
P-Value =

Answer 1

From the given proportions the expected frequencies are first computed as:
Total Frequency = 17 + 25 + 6 + 16 = 64

E(A) = 0.1*64 = 6.4
E(B) = 0.5*64 = 32
E(C) = 0.1*64 = 6.4
E(D) = 0.3*64 = 19.2

The chi square test statistic here is obtained as:

Therefore 19.6458 is the required chi square test statistic value here.

b) For n - 1 = 3 degrees of freedom, the p-value here is obtained from the chi square distribution tables as:

Therefore 0.0002 is the required p-value here.