You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:
HoHo : pA=.2pA=.2; pB=.2pB=.2; pC=.3pC=.3; pD=0.3pD=0.3
Complete the table. Report all answers accurate to three decimal
places.
Category | Observed Frequency |
Expected Frequency |
---|---|---|
A | 19 | |
B | 30 | |
C | 30 | |
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 0.01,
What would be the conclusion of this hypothesis test?
Report all answers accurate to three decimal places.
ANSWER & EXPLANATION
VARIABLES | OBSERVED | PROBABILITY | EXPECTED = (P*TOTAL) | Q |
A | 19 | 0.2 | (111*0.2) = 22.2 | 0.4612 |
B | 30 | 0.2 | 22.2 | 2.7405 |
C | 30 | 0.3 | 33.3 | 0.3270 |
D | 32 | 0.3 | 33.3 | 0.0507 |
TOTAL | 111 | 1 | 111 | 3.5794 |
CHI-SQUARE VALUE = 3.5794
The P-Value is .3106 At 3 DF.
The result is not significant at p < .01
The P value is 0.3 > significance level is 0.01. Here
The P value is greater than the significance level so there is sufficient evidence to
Fail to reject the Null Hypothesis
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