Question

In: Statistics and Probability

The production department of Celltronics International wants to explore the relationship between the number of employees...

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 =

Solutions

Expert Solution

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)


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