During a recent exhibit on the physics of football, volunteers at the local science museum conducted a survey of 575 randomly chosen visitors. The survey included questions about attendance at sporting events. The volunteers calculated a 90% confidence interval of for the mean number of sporting events museum visitors attended last year. Is the following conclusion valid? If 100 more surveys are conducted (each using a sample with members chosen randomly and independently), it is expected that exactly 90 of them will each produce a 90% confidence interval that contains its sample mean. Choices: (A)yes (B)no

Question

During a recent exhibit on the physics of football, volunteers at the local science museum conducted a survey of 575 randomly chosen visitors. The survey included questions about attendance at sporting events. The volunteers calculated a 90% confidence interval of  for the mean number of sporting events museum visitors attended last year.  Is the following conclusion valid? If 100 more surveys are conducted (each using a sample with members chosen randomly and independently), it is expected that exactly 90 of them will each produce a 90% confidence interval that contains its sample mean.    Choices: (A)yes (B)no

Bytelearn · Accepted Answer

Conclusion Misinterpretation: The conclusion suggests that if 100 more surveys are conducted, exactly 90 of them will contain the true mean within their 90% confidence intervals.Understanding Confidence Intervals: This understanding of confidence intervals is incorrect. A 90% confidence interval means that if we were to take many samples and calculate a confidence interval for each sample, about 90% of these intervals would contain the true population mean.Random Sampling Variability: It does not guarantee that in any given set of 100 surveys, exactly 90 will contain the true mean. The actual number could be higher or lower due to random sampling variability.Invalid Conclusion: Therefore, the conclusion that exactly 90 out of 100 confidence intervals will contain the true mean is not valid.

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