Answer-first summary for fast verification
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. At the 95% confidence level, the critical value is given as 5.99. **Decision Rule:** - If JB statistic > 5.99, we reject the null hypothesis that the data is normally distributed - If JB statistic ≤ 5.99, we fail to reject the null hypothesis **Analysis of each dataset:** - **Dataset A**: JB = 5.90 ≤ 5.99 → Fail to reject null (likely normal) - **Dataset B**: JB = 6.02 > 5.99 → Reject null (not normal) - **Dataset C**: JB = 3.16 ≤ 5.99 → Fail to reject null (likely normal) - **Dataset D**: JB = 6.35 > 5.99 → Reject null (not normal) **Conclusion:** - Datasets that are likely NOT drawn from a normal distribution: **B and D** - This corresponds to **Option D** 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.
Author: LeetQuiz .
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
No comments yet.