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Rudolph Bulbs Inc. is testing the long term reliability of its holiday lights. They powered a random sample of 525525 identical light strands from a recent production batch for 10,00010,000 hours. Afterward, the number of dead bulbs in each strand was recorded. Based on the test, a 99%99\% confidence interval of was calculated for the mean number of dead bulbs in a light strand from the production batch after 10,00010,000 hours.\newlineIs the following conclusion valid?\newlineIf 100100 more samples are taken (with elements chosen randomly and independently), it is expected that exactly 9999 of them will each produce a 99%99\% confidence interval that contains its sample mean.\newlineChoices:\newline(A)yes\newline(B)no\newline

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Q. Rudolph Bulbs Inc. is testing the long term reliability of its holiday lights. They powered a random sample of 525525 identical light strands from a recent production batch for 10,00010,000 hours. Afterward, the number of dead bulbs in each strand was recorded. Based on the test, a 99%99\% confidence interval of was calculated for the mean number of dead bulbs in a light strand from the production batch after 10,00010,000 hours.\newlineIs the following conclusion valid?\newlineIf 100100 more samples are taken (with elements chosen randomly and independently), it is expected that exactly 9999 of them will each produce a 99%99\% confidence interval that contains its sample mean.\newlineChoices:\newline(A)yes\newline(B)no\newline
  1. Interpreting 9999\% Confidence Interval: A 99%99\% confidence interval means that we can be 99%99\% confident that the true mean number of dead bulbs lies within the calculated interval.
  2. Incorrect Conclusion: The conclusion states that if 100100 more samples are taken, exactly 9999 of them will contain the true mean within their 99%99\% confidence intervals.
  3. Clarification Needed: This interpretation is incorrect. A 99%99\% confidence interval does not guarantee that 9999 out of 100100 confidence intervals from new samples will contain the true mean.
  4. Correct Interpretation: The correct interpretation is that we can be 99%99\% confident that the confidence interval from a single sample contains the true mean. It does not predict the outcomes of future samples.

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