Boston Electric Generators has been getting many complaints from its major$$ customer, Home$$ Station, about the quality of its shipments of home generators. Daniel$$ Shimshak, the plant$$ manager, is alarmed that a customer is providing him with the only information the company has on shipment quality. He decides to collect information on defective shipments through a form he has asked his drivers to complete on arrival at$$ customers' stores. The forms for the first $285$ shipments have been turned in$.$ They show the following over the past $8$ weeks:

Week

No$.$ of

Shipments

No$.$ of

Shipments with Defects

Reason for Defective Shipment

Incorrect

Bill of

Lading

Incorrect

Truckload

Damaged

Product

Trucks

Late

$1$

$23$

$10$

$2$

$0$

$4$

$4$

$2$

$31$

$11$

$1$

$4$

$1$

$5$

$3$

$32$

$12$

$2$

$0$

$4$

$6$

$4$

$39$

$13$

$1$

$2$

$5$

$5$

$5$

$35$

$12$

$2$

$1$

$4$

$5$

$6$

$40$

$14$

$3$

$0$

$5$

$6$

$7$

$41$

$14$

$4$

$0$

$4$

$6$

$8$

$44$

$16$

$2$

$2$

$4$

$8$

This exercise contains only part a$.$

$$a$)$ Choose the correct scatter diagram below using total number of shipments and number of defective shipments.

A$.$

$20$

$26$

$32$

$38$

$44$

$50$

$0$

$10$

$20$

Shipments

Defective Shipments

A scatterplot with shipments on the x$-$axis from $20$ to $50$ in $2-$unit increments and defective shipments on the y$-$axis from $0$ to $20$ in $2-$unit increments. The points for a downward$-$sloping line.

B$.$

$20$

$26$

$32$

$38$

$44$

$50$

$0$

$10$

$20$

Shipments

Defective Shipments

A scatterplot with shipments on the x$-$axis from $20$ to $50$ in $2-$unit increments and defective shipments on the y$-$axis from $0$ to $20$ in $2-$unit increments. The points for an upward$-$sloping line.

C$.$

$20$

$26$

$32$

$38$

$44$

$50$

$0$

$10$

$20$

Shipments

Defective Shipments

A scatterplot with shipments on the x$-$axis from $20$ to $50$ in $2-$unit increments and defective shipments on the y$-$axis from $0$ to $20$ in $2-$unit increments. The points form a curve that slopes down and then up$.$

D$.$

$20$

$26$

$32$

$38$

$44$

$50$

$0$

$10$

$20$

Shipments

Defective Shipments

A scatterplot with shipments on the x$-$axis from $20$ to $50$ in $2-$unit increments and defective shipments on the y$-$axis from $0$ to $20$ in $2-$unit increments. The points form a line that is almost horizontal.

Part $2$

The scatter diagram shows

$$

a strong negative

a strong positive

no

relationship between the variables.