Question

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

HoHo : pA=0.3pA=0.3;  pB=0.2pB=0.2;  pC=0.2pC=0.2;  pD=0.3pD=0.3

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

Category	Observed Frequency	Expected Frequency
A	28
B	15
C	40
D	32

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

What is the P-Value?
P-Value =


For significance level alpha 0.005,

What would be the conclusion of this hypothesis test?

• Fail to reject the Null Hypothesis
• Reject the Null Hypothesis

Report all answers accurate to three decimal places.

Answer 1

The statistic software output for this problem is:

Chi-Square goodness-of-fit results: Observed: Observed Expected: E N DF Chi-Square P-value 115 3 16.753623 0.0008 Observed – Expected 34.5 23 34.5

$\chi^2$ = 1.753

P-value = 0.0008

P-value < 0.005

Reject the Null Hypothesis