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 12 during a one-hour period. Then 5 employees assembled them. They produced 20 during a one-hour period. The complete set of paired observations follows.

Number of Assemblers	One-Hour Production (units)
3	12
5	20
2	6
6	25
4	17

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

  
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b.	A scatter diagram is provided below. Based on it, does there appear to be any relationship between the number of assemblers and production?

	(Click to select)NoYes , as the number of assemblers (Click to select)decreasesincreases, so does the production.

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

X	Y			( )2	( )2	( )( )
3	12		-4		16
5	20	1		1		4
2	6		-10		100
6	25	2		4		18
4	17		1	0		0

=

=

sx

=

sy

=

r

=

Answer 1

X	Y	X-xbar	Y-ybar	(X-xbar )2	( Y-ybar)2	( X-xbar)(Y-ybar )
3	12	-1	-4	1	16	4
5	20	1	4	1	16	4
2	6	-2	-10	4	100	20
6	25	2	9	4	81	18
4	17	0	1	0	1	0
xbar=sum(X)/n	4
ybar=Sum(Y)/n	16
s^2y=(sum(Y-ybar)^2)/(n-1)	53.5	sy=sqrt(s^2y)	7.3144
s^2x=(sum(X-xbar)^2)/(n-1)	2.5	sx=sqrt(s^2x)	1.5811	=Sxy/(Sx*Sy)	=0.9944
Sxy=(sum((X-xbar)(Y-ybar)))/(n-1)	11.5

From the scatter plot there is positive relationship between the number of assemblers and production.

means as number of assemblers increases the production is also increases . (Yes and Increases)