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Answer: Dataset B and D
## 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. **Given:** - Critical value at 95% confidence level = 5.99 - If JB statistic > 5.99, we reject the null hypothesis (that the data is normally distributed) **Analysis of each dataset:** - **Dataset A**: JB = 5.90 < 5.99 → Cannot reject null hypothesis (likely normal) - **Dataset B**: JB = 6.02 > 5.99 → Reject null hypothesis (not normal) - **Dataset C**: JB = 3.16 < 5.99 → Cannot reject null hypothesis (likely normal) - **Dataset D**: JB = 6.35 > 5.99 → Reject null hypothesis (not normal) **Conclusion:** Datasets B and D have JB statistics exceeding the critical value of 5.99, indicating they are likely not drawn from a normal distribution.
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| 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