Consider the picture below. This is a graphical presentation of the mean and 50

Question

Consider the picture below. This is a graphical presentation of the mean and 50 confidence intervals. Notice that some of the confidence intervals don’t capture the mean. In fact, the graph indicates that 7 of the confidence intervals don’t capture the true value of mu. The fact that there are 50 confidence intervals, and the mean is 50 is merely a coincidence. What percentage of the confidence intervals captured the true value of mu? _____________    Given that the level of confidence is 90%, is the answer to the previous question reasonable?

Explanation / Answer

The graphical representation has not been provided, but taking into consideration the data provided:

Total no. of CI = 50

CI which don’t capture the true value of mu = 7

Hence, CI which do capture the true value of mu = 50-7 = 43

Therefore, (43/50) x 100 = 86% of the CI capture the true value of mu. (Ans.)

Given that the level of confidence is 90%, the answer to the previous question is not totally unreasonable since 86 is quite close to 90, but it is still quite a bit of an approximation.

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