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 x-value 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 two-tailed 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?

*librarians intial claim

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.

To determine if the value of 4 checkouts per year is an outlier, we need to compare it to the mean and standard deviation of the data.

We are given that the librarian claims the mean number of checkouts per book per year is seven. Let's assume this claim is true.

The standard deviation of the number of checkouts per book per year is given as approximately 0.90. This standard deviation represents the average amount of variation or spread around the mean.

To determine if a specific value is an outlier, we need to understand how it deviates from the mean in terms of standard deviations.

To do this, we will calculate the z-score for the value of 4 checkouts:

z = (x - mean) / standard deviation

Here, x is the value of 4 checkouts, the mean is 7, and the standard deviation is approximately 0.90.

z = (4 - 7) / 0.90
z = -3.33

The z-score tells us how many standard deviations away from the mean the value of 4 checkouts is. In this case, the value is 3.33 standard deviations below the mean.

Typically, a common threshold for identifying outliers is when a value is more than 2 or 3 standard deviations away from the mean. Since the value of 4 checkouts is 3.33 standard deviations below the mean, it can be considered an outlier.

Therefore, in this case, the value of 4 checkouts per year would be considered an outlier if the mean number of checkouts per book per year is indeed 7, as claimed by the librarian.