Air Force pilots have a higher than normal hearing loss due to the noise levels

Question

Air Force pilots have a higher than normal hearing loss due to the noise levels they are exposed to in cockpits. In particular the T-37 aircraft is notorious for high decibel readings. A sample of 30 T-37s produced the following 95% lower confidence interval for the true mean noise level (in decibels) of all T-37s: p 2 85 decibels. A young pilot interprets this confidence interval as meaning 95% of all T-37 aircraft have a cockpit decibel reading of 85 or greater. Is this interpretation correct? Why or why not? 5.30

Explanation / Answer

This interpretation is not correct.

The biggest misconception regarding confidence intervals is that they represent the percentage of data from a given sample that falls between the upper and lower bounds. For example, one might erroneously interpret the aforementioned 95% confidence interval as indicating that 95% of the data in a random sample falls between these numbers. This is incorrect, though a separate method of statistical analysis exists to make such a determination. Doing so involves identifying the sample's mean and standard deviation and plotting these figures on a bell curve. The confidence level describes the uncertainty associated with a sampling method. A 90% confidence level means that we would expect 90% of the interval estimates to include the population parameter.

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