Statistics
posted by Lindy on .
The head librarian claims that books have been checked out an average of seven times in the last year.
You suspect she has exaggerated the checkout rate and that the mean number of checkouts per book per year is, in fact, less than seven.
Using the computerized card catalog, you randomly select one book and find that it has been checked out four times in the last year. Assume that the standard deviation of the number of checkouts per book per year is approximately 0.90.
If the mean number of checkouts per book per year is seven, as the librarian claims, would you consider a value of 4 checkouts per year to be an outlier?
Is the x value of interest more than 3 standard deviations below the mean or is it 3 st deviations above the mean?
Or is the xvalue not an outlier?

First of all, what criterion are you using to identify an outlier?
If it is Z = ±3, then this book would be an outlier. For outliers, it is a twotailed test, you are interested in extremely deviant scores both above and below the mean.
I hope this helps. Thanks for asking. 
Thanks. Would that mean the initial claim was too high?

Among the thousands of books that are checked out, the one outlier would have a minimal effect, if at all. This is inadequate evidence to respond to the librarian's sstatistic.
To test the The Ho that μ = 7 against the alternative hypothesis that μ < 7, a larger sample is needed to compare the sample mean to the librarian's estimate.
I hope this helps a little more. Thanks for asking. 
*librarians intial claim