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A major insurance company wants to estimate the effort it would take to completely switch to paper-free correspondence. The company randomly selected 300300 customers and logged the number of letters sent to each last month. They found a 95%95\% confidence interval of for the mean number of letters sent to each customer last month.\newlineIs the following conclusion valid?\newlineIf the company takes another random sample, there is a 95%95\% chance that the mean number of letters sent to each customer last month will be in the new sample's 95%95\% confidence interval.\newlineChoices:\newline(A)yes\newline(B)no

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Interpret confidence intervals for population meansright chevron icon

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Q. A major insurance company wants to estimate the effort it would take to completely switch to paper-free correspondence. The company randomly selected 300300 customers and logged the number of letters sent to each last month. They found a 95%95\% confidence interval of for the mean number of letters sent to each customer last month.\newlineIs the following conclusion valid?\newlineIf the company takes another random sample, there is a 95%95\% chance that the mean number of letters sent to each customer last month will be in the new sample's 95%95\% confidence interval.\newlineChoices:\newline(A)yes\newline(B)no
  1. Understand Confidence Interval: Understand the concept of a confidence interval. A 95%95\% confidence interval means that if we were to take many samples and build a confidence interval from each of them, 95%95\% of those intervals would contain the true mean.
  2. Analyze Conclusion: Analyze the given conclusion.\newlineThe conclusion suggests that a new sample's mean will fall within the previously calculated confidence interval 95%95\% of the time, which is a misunderstanding of what a confidence interval represents.
  3. Identify Error: Identify the error in reasoning.\newlineThe correct interpretation is that 95%95\% of such confidence intervals from repeated random samples will contain the true population mean, not that a new sample's mean will fall within a specific previously calculated interval.
  4. Choose Correct Answer: Choose the correct answer based on the analysis.\newlineThe conclusion given is not valid, so the answer is (B)(B) no.

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