What is the chi-square test-statistic for this data? χ2=χ2= What is the P-Value? P-Value = For significance level alpha 0.05, What would be the conclusion of this hypothesis test? Reject the Null Hypothesis Fail to reject the Null Hypothesis
You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:HoHo : pA=0.2pA=0.2; pB=0.3pB=0.3; 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 | 30 | |
| B | 42 | |
| C | 18 | |
| 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 0.05,
What would be the conclusion of this hypothesis test?
- Reject the Null Hypothesis
- Fail to reject the Null Hypothesis
Report all answers accurate to three decimal places.
The test hypotheses are given below:
H0: The distributions are the same (H0 : pA=0.2; pB=0.3; pC=0.2; pD=0.3
). H1: The distributions are different.
The test statistic is calculated by the formula,
χ2=∑(O−E)2/E
Where, O represents the observed frequency and E represents the expected frequency.
Methods for finding the expected frequency:
Method 1: If the all the expected frequencies are equal, then E=nk
Method 2: If the expected frequencies are not equal, then E=np for each category.
Where, n is the total number of frequencies, k is the categories and p is the probability of occurrence.
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