SOLUTION: Cathy wishes to estimate the mean height of women aged 18-24. She picks a sample of 100 women aged between 18 and 24 and constructs a 99% confidence interval for the population mea

Question 1108904: Cathy wishes to estimate the mean height of women aged 18-24. She picks a sample of 100 women aged between 18 and 24 and constructs a 99% confidence interval for the population mean. If she were to repeat this procedure 200 times in total, she would obtain 200 different confidence intervals.
(a)How many of these intervals would you expect to contain the population mean �mu�?
(b) Explain your reason

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
I would expect 99%*200 or 198 of the intervals to contain the mean.
If this is done with a parameter that cannot ever be known, then 99% of the intervals will contain the parameter. We just don't know which 99%.

A confidence interval of a parameter gives an interval in which the parameter is expected to be found. Because the interval either contains or doesn't contain the parameter, the probability is either 0 or 100%, which is not helpful. Remember that the parameter is unknown and unknowable in most cases. We therefore use high, medium or low confidence and can use percentages. They are not probabilities but measures of how confident we are. The percentage aspect comes into place should we construct many confidence intervals, which typically we do not. A 95% CI says that if we construct 100 intervals, 95% will contain the parameter. That is a true percentage, not a confidence. We don't know which 95, however, since the parameter is still unknown or unknowable. For a single interval, we use confidence.
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