Question

The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, 3 employees were assigned to assemble the subassemblies. They produced 14 during a one-hour period. Then 5 employees assembled them. They produced 23 during a one-hour period. The complete set of paired observations follows.

Number of Assemblers				One-Hour Production (units)
	3				14
	5				23
	2				9
	6				38
	4				26

The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees.

1. Draw a scatter diagram.

1. On the graph below, use the point tool to plot the point corresponding to the first Number of Assemblers and her Production (No of Assemblers1).

2. Repeat the process for the remainder of the sample (No of Assemblers2, No of Assemblers3, … ).

3. To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.

2. Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production?

3. Compute the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round s_x, s_y and r to 3 decimal places.)

x				y				(x−x⎯⎯)x-x¯				(y−y⎯⎯)y-y¯				(x−x⎯⎯)2x-x¯2				(y−y⎯⎯)2y-y¯2				(x−x⎯⎯) (y−y⎯⎯)x-x¯ y-y¯
	3				14								-8								64
	5				23				1								1								1
	2				9								-13								169
	6				38				2								4								32
	4				26								4				0								0

x⎯⎯x¯

=

y⎯⎯y¯

=

Sx

=

Sy

=

r

=

Answer 1

The scatter diagram is:

There is a strong positive relationship between the number of assemblers and production.

xbar	ybar	Sx	Sy	r
4	22	1.581	11.247	0.942

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