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Suggested answer to exercise: Confidence interval in the talking time study

"Of the 330 patients who provided sociodemographic data,
. . . mean age was 42.9 years (SD 18.2 (95% confidence interval 17 to 84) years)

Question: What is wrong with this confidence interval?

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Suggested answer

This is not a confidence interval for the mean or the standard deviation.
The 95% confidence interval for the mean would be much narrower, 40.9 to 44.9 years.
The 95% confidence interval for the standard deviation would be expected to have
the standard deviation itself near the middle and also to much narrower.
After all, the standard deviation for age could not plausibly be 78.6 years,
as mean age plus two standard deviations would be 200 and mean minus
two standard deviations would be minus 114 years, both impossible.
In fact, the 95% confidence interval for the standard deviation would be 16.8 to 19.6 years.

I suspect that 17 to 84 years is the range and that the youngest patient was 17 years old.

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Last updated: 19 January, 2009.

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