A survey of 30 emergency room patients found that the average waiting time was 1

Question

A survey of 30 emergency room patients found that the average waiting time was 174.3 minutes. A 95% confidence interval for mu was found to be (152.4, 196.2). The following is an incorrect interpretation of the interval: "We are 95% confident that the waiting time of all emergency room patients sampled is between 152.4 minutes and 196.2 minutes." (a) In the interpretation above, one word is missing. What is the missing word? (b) There is also one word in the interpretation that does not belong there, and it needs to be removed to make the interpretation correct. What word needs to be removed?

Explanation / Answer

Interpreting the Confidence interval

It is interpreted as containing the parameter it is estimating with 95% confidence.

The word Sampled is totally wrong. So we must replace this word by esimated

An interval estimate of a parameter is an interval or range of values used to estimate the parameter.

This estimate may or may not contain the value of parameter being estimated.

Or if sampling was repeated, 95% of CI s produced will contain the parameter being estimated.

a) Estimated is the missing word.

b) The word sampled must be replaced by the word estimated

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