Maureen is an epidemiologist interested in how the common cold impacts health clinics. She asked 225 randomly selected clinics across California for their patient data from one specific month. For each clinic, she looked at the number of patients who came in with a common cold that month. Maureen found a 90% confidence interval of for the mean number of patients with a common cold who visited clinics in California that month. Is the following conclusion valid? If Maureen takes another random sample, there is a 90% chance that the mean number of patients with a common cold who visited clinics in California that month will be in the new sample's 90% confidence interval. Choices: (A)yes (B)no

Question

Maureen is an epidemiologist interested in how the common cold impacts health clinics. She asked 225 randomly selected clinics across California for their patient data from one specific month. For each clinic, she looked at the number of patients who came in with a common cold that month. Maureen found a 90% confidence interval of  for the mean number of patients with a common cold who visited clinics in California that month.  Is the following conclusion valid? If Maureen takes another random sample, there is a 90% chance that the mean number of patients with a common cold who visited clinics in California that month will be in the new sample's 90% confidence interval.    Choices: (A)yes (B)no

Bytelearn · Accepted Answer

Definition of Confidence Intervals: Confidence intervals provide a range of values that you can be certain percent confident contains the population parameter. In this case, it's the mean number of patients with a common cold visiting clinics.Common Misunderstanding: The conclusion that there is a 90% chance that the mean number of patients with a common cold who visited clinics in California that month will be in the new sample's 90% confidence interval is a common misunderstanding of confidence intervals.Correct Interpretation: The correct interpretation is that if we were to take many samples and build a 90% confidence interval from each of them, then 90% of those intervals would contain the true population mean.Single Sample Confidence: Therefore, the conclusion that any single new sample's 90% confidence interval will contain the true mean with a 90% chance is incorrect. Each new sample's confidence interval might or might not contain the true mean, and the 90% confidence level doesn't apply to the intervals of individual samples in this way.

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