A Company Must Decide Which of Two Delivery Services They

Multiple Choice

A company must decide which of two delivery services they will contract with.During a recent trial period they shipped numerous packages with each service,and have kept track of how often deliveries did not arrive on time.Here are the data: $$\begin{array} { c | c c c } \begin{array} { c } \text { Delivery } \\\text { service }\end{array} & \begin{array} { c } \text { Type of } \\\text { service }\end{array} & \begin{array} { c } \text { Number of } \\\text { deliveries }\end{array} & \begin{array} { c } \text { Number of } \\\text { late packages }\end{array} \\\hline & \text { Regular } & 100 & 3 \\\text { Super Ship }& \text { Overnight } & 400 & 40 \\\hline & \text { Regular } & 400 & 16 \\\text { Fast Paks } & \text { Overnight } & 100 & 14\end{array}$$ Based on the results,the company decided to hire Fast Paks.Do you agree they deliver on time more often? Explain.

A) Yes.Fast Paks only delivers 3% of its regular packages late,compared to Super Ship,who deliver 4% of its regular packages late.Additionally,Fast Paks only delivers 10% of its overnight packages late,compared to Super Ship,who delivers 14% of its overnight packages late.Fast Paks is better at delivering regular and overnight packages.
B) No.Super Ship only delivers 3% of its regular packages late,compared to Fast Paks,who deliver 4% of its regular packages late.Additionally,Super Ship only delivers 10% of its overnight packages late,compared to Fast Paks,who delivers 14% of its overnight packages late.Super Ship is better at delivering regular and overnight packages.
C) No.Fast Paks only delivers 0.09% of its packages late,compared to Super Ship,who delivers 0.06% of its packages late.Super Ship is better at delivering regular and overnight packages.
D) Yes.Fast Paks only delivers 0.06% of its packages late,compared to Super Ship,who delivers 0.09% of its packages late.Fast Paks is better at delivering regular and overnight packages.
E) No.This is an example of Simpson's paradox and unfair averaging.Since the overall percentages and the individual percentages disagree on which delivery service is better,both services can be considered equal.It cannot be determined whether Super Ship or Fast Paks deliver packages on time more often.