A quality engineer at a consumer electronics company wants to know whether the defects per television set are from a Poisson distribution. The engineer randomly selects 300 televisions and records the number of defects per television.
The null hypothesis states that the data follow a Poisson distribution. Because the p-value is 0.000, which is less than the significance level of 0.05, the engineer rejects the null hypothesis and concludes that the data do not follow a Poisson distribution. The graphs indicate that the difference between the observed and expected values is large for categories 1 and 3, and that category 3 is the highest contributor to the chi-square statistic.
Frequencies in Observed |
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N | Mean |
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300 | 0.536667 |
Defects | Poisson Probability | Observed Count | Expected Count | Contribution to Chi-Square |
---|---|---|---|---|
0 | 0.584694 | 213 | 175.408 | 8.056 |
1 | 0.313786 | 41 | 94.136 | 29.993 |
2 | 0.084199 | 18 | 25.260 | 2.086 |
>=3 | 0.017321 | 28 | 5.196 | 100.072 |
Null hypothesis | H₀: Data follow a Poisson distribution |
---|---|
Alternative hypothesis | H₁: Data do not follow a Poisson distribution |
DF | Chi-Square | P-Value |
---|---|---|
2 | 140.208 | 0.000 |