what are the frequency, test statistic, and critical value?

Question

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

 H0 : Pa=0.25;  Pb=0.25;  Pc=0.4;  Pd=0.1 

Give all answers as decimals rounded to 3 places after the decimal point, if necessary.

Complete the table:

CategoryObserved	FrequencyExpected	Frequency
A	18
B	21
C	37
D	14

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

Test Statistic: X2= 

For a significance of level alpha = 0.01, what is the chi-square critical value?

Critical Value: X2= 

Answer 1

A= .25 *90, B=.25*90, C=.4*90, D=.1*90. In each case compute (o-e)^2/e and sum to get 3.805 which is not signicant at p < .05. The critical value for .01 at 3 df is 11.35.