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An inspector at the Yummy Treat candy factory wanted to make sure the chocolate bonbons it produces weigh the correct amount. On a particular day, he weighed 7575 randomly selected bonbons from the production line. From the data, the inspector calculated a 99%99\% confidence interval of for the mean weight of bonbons produced that day (in grams).\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. An inspector at the Yummy Treat candy factory wanted to make sure the chocolate bonbons it produces weigh the correct amount. On a particular day, he weighed 7575 randomly selected bonbons from the production line. From the data, the inspector calculated a 99%99\% confidence interval of for the mean weight of bonbons produced that day (in grams).\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. Confidence Interval Misunderstanding: The inspector's conclusion seems to be a misunderstanding of what a confidence interval represents. A 99%99\% confidence interval means that if we were to take many samples and calculate the confidence interval for each, we would expect 99%99\% of those intervals to contain the true population mean, not necessarily the sample mean.
  2. Incorrect Statement: The statement that exactly 9999 out of 100100 more samples will produce a 99%99\% confidence interval containing their sample mean is incorrect. Each sample has a 99%99\% chance of its confidence interval containing the population mean, but this does not guarantee that exactly 9999 out of 100100 samples will do so.
  3. Correct Interpretation: The correct interpretation is that we are 99%99\% confident that the interval calculated from the sample data contains the true population mean. It does not predict the outcomes of future samples.

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