Explanation:
The Jarque-Bera (JB) test is used to test whether a dataset follows a normal distribution. The test statistic follows a chi-squared distribution with 2 degrees of freedom. At the 95% confidence level, the critical value is given as 5.99.
Decision Rule:
Analysis of each dataset:
Conclusion:
The key insight is that even though Datasets A and B have identical skewness and kurtosis values, the different sample sizes (T) result in different JB statistics, with Dataset B exceeding the critical value while Dataset A does not.
Ultimate access to all questions.
The following data is collected for four distributions:
| Dataset | Skew | Kurtosis | T | JB |
|---|---|---|---|---|
| A | 0.85 | 3.00 | 50 | 5.90 |
| B | 0.85 | 3.00 | 51 | 6.02 |
| C | 0.35 | 3.35 | 125 | 3.16 |
| D | 0.35 | 3.35 | 250 | 6.35 |
Which of these datasets are likely (at the 95% confidence level, the chi-squared critical value is 5.99) to not be drawn from a normal distribution?
A
Dataset A and C
B
Dataset B and C
C
Dataset A and D
D
Dataset B and D
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