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Drinkers of Jitterfuel iced tea complain that the amount of caffeine per bottle varies too much. Jitterfuel decided to test these claims by measuring the amount of caffeine in 125125 randomly selected bottles from the latest production batch. The company found a 95%95\% confidence interval of for the mean amount of caffeine in bottles from the production batch (in milligrams).\newlineIs the following conclusion valid?\newlineIf 100100 more samples are taken (with elements chosen randomly and independently), it is expected that exactly 100100 of them will each produce a 95%95\% confidence interval that contains its sample mean.\newlineChoices:\newline(A)yes\newline(B)no

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Q. Drinkers of Jitterfuel iced tea complain that the amount of caffeine per bottle varies too much. Jitterfuel decided to test these claims by measuring the amount of caffeine in 125125 randomly selected bottles from the latest production batch. The company found a 95%95\% confidence interval of for the mean amount of caffeine in bottles from the production batch (in milligrams).\newlineIs the following conclusion valid?\newlineIf 100100 more samples are taken (with elements chosen randomly and independently), it is expected that exactly 100100 of them will each produce a 95%95\% confidence interval that contains its sample mean.\newlineChoices:\newline(A)yes\newline(B)no
  1. Understand Confidence Interval Definition: Understand what a 95%95\% confidence interval means. It implies that if we were to take many samples and calculate the confidence interval for each, about 95%95\% of these intervals would contain the true population mean.
  2. Analyze Given Conclusion: Analyze the conclusion given. It states that if 100100 more samples are taken, exactly 100100 of them will produce a 95%95\% confidence interval that contains its sample mean. This is a misunderstanding of confidence intervals.
  3. Recognize Error in Conclusion: Recognize the error in the conclusion. The correct interpretation is that we expect about 9595 out of 100100 samples to produce a confidence interval that contains the population mean, not the sample mean as stated.
  4. Choose Correct Answer: Choose the correct answer based on the analysis. The conclusion is not valid because it misinterprets the meaning of a 95%95\% confidence interval.

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