Final answer:
The 95% confidence interval for Eden's mark is (61.12, 72.88). This means we can be 95% confident that her true mark falls within this range. If Eden completes a new exam consisting of 8 folds of the original exam, the reliability of the new exam would be approximately 10.3%, and the confidence interval for her mark based on the new reliability would be wider.
Step-by-step explanation:
The 95% confidence interval for Eden's mark can be calculated by finding the margin of error and adding or subtracting it from her actual mark. The formula for the margin of error is z * (standard deviation / sqrt(sample size)), where z is the z-score corresponding to the desired level of confidence. For a 95% confidence level, the z-score is approximately 1.96. Given that the reliability of the exam is 0.66 and the standard deviation is 10, we can use the formula for the margin of error to find that the margin of error is approximately 1.96 * (10 / sqrt(1-0.66)) = 1.96 * (10 / sqrt(0.34)) ≈ 5.88. Therefore, the 95% confidence interval for Eden's mark is (67 - 5.88, 67 + 5.88), which simplifies to (61.12, 72.88).
The interval [61.12, 72.88] represents the range of values within which we can be 95% confident that Eden's true mark lies. This means that if we were to repeat the experiment multiple times and calculate the confidence interval each time, we would expect approximately 95% of the intervals to contain the true mark. In other words, we are fairly certain that Eden's mark falls within this range.
If Eden completes a new exam consisting of 8 folds of the original exam, the reliability of the new exam can be calculated using the rule of serial testing. The formula for the reliability of a test with multiple folds is r^k, where r is the reliability of a single fold and k is the number of folds. In this case, the reliability of the new exam would be 0.66^8 ≈ 0.103, or approximately 10.3%. Using this reliability value, we can calculate the 95% confidence interval for Eden's mark based on the new exam. Since the reliability is lower, the margin of error will be larger. Therefore, the new confidence interval will be wider than the previous one.