Chapter 18, Problem 19E

To determine

To explain does a college where $\text{522 of the 603}$ freshmen returned the next year as sophomores have a right brag that it has unusually high retention rate.

Answer to Problem 19E

Yes, the college should have rights to brag because its retention right is nearly $7$ standard deviations above mean retention rate.

Explanation of Solution

It is given in the question that the company reported that the national college freshmen-to-sophomore retention rate held steady at $74\%$ over the previous four years. Now, from a college $\text{522 of the 603}$ freshmen returned the next year as sophomores. Thus, let us first calculate the mean and the standard deviation as:

  $\begin{array}{l}\mu =p=0.74\\ \sigma =\sqrt{\frac{pq}{n}}\\ =\sqrt{\frac{0.74(0.26)}{603}}\\ =0.018\end{array}$

Therefore, from the z -score we have that,

  $\begin{array}{l}z=\frac{\frac{522}{603}-0.74}{0.018}\\ =6.982\end{array}$

Thus, we conclude that the college should have rights to brag because its retention right is nearly $7$ standard deviations above mean retention rate.