Chapter 3, Problem 38E

(a)

To determine

To Explain: the two services overall percentage of late deliveries.

Explanation of Solution

Given:

Delivery service	type of service	number of deliveries	number of late packages
Pack Rats	Regular	400	12
	Overnight	100	16
Boxes R us	Regular	100	2
	Overnight	400	28

Calculation:

For pack rats services

Total number of deliveries 400+100=500

Number of late package 12+16=28

Late deliveries for pack rats

  $\begin{array}{l}=\frac{28}{500}\times 100\\ =5.6\%\end{array}$

For Boxes R US services

Total number of deliveries 400+100=500

Number of late packages 2+28=30

  $\begin{array}{l}=\frac{30}{500}\times 100\\ =6\%\end{array}$

Therefore the overall percentage of late delivery is slightly lower for Pack Rats service (5.6%) in comparison to Boxes R US service (6%).

(b)

To determine

To Explain: that pack rats delivers on time more often, agree or not.

Explanation of Solution

Given:

Delivery service	type of service	number of deliveries	number of late packages
Pack Rats	Regular	400	12
	Overnight	100	16
Boxes R us	Regular	100	2
	Overnight	400	28

By seeing the part (a), it is observed that it could conclude that pack rats deliver more often on time but there is difference between the late deliveries of packages.

(c)

To determine

To find: the phenomenon of the result here are an instance.

Explanation of Solution

Given:

Delivery service	type of service	number of deliveries	number of late packages
Pack Rats	Regular	400	12
	Overnight	100	16
Boxes R us	Regular	100	2
	Overnight	400	28

By seeing the result, it is observed that the results are an instance of Simpson’s Paradox phenomenon.