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, 2 employees were assigned to assemble the subassemblies. They produced 11 during a one-hour period. Then 4 employees assembled them. They produced 18 during a one-hour period. The complete set of paired observations follows.
Number of Assemblers One-Hour Production (units)
2 11
4 18
1 7
5 29
3 20
The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees.
a. Draw a scatter diagram.
b. Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production? Explain.
c. Compute the correlation coefficient.

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

Number of Assemblers(x) One-Hour Production(y) (units)

2 11

4 18

1 7

5 29

3 20

a. Draw a scatter diagram.

Solution : Refer the attached figure

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

Solution: The equation that shows the relationship between the number of assemblers and production is [tex]y=5.1x+1.7[/tex]

Where y is One-Hour Production (units) and x is the Number of Assemblers

c.Compute the correlation coefficient.

Solution:

Formula of correlation coefficient:[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{[n \sum x^2 -(\sum x)^2][n \sum y^2 -(\sum y)^2]}[/tex]

x y xy [tex]x^2[/tex] [tex]y^2[/tex]

2 11 22 4 121

4 18 72 16 324

1 7 7 1 49

5 29 145 25 841

3 20 60 9 400

Sum: 15 85 306 55 1735

n=5

Substitute the values in the formula :

[tex]r=\frac{5(306)-(15)(85)}{[5 (55) -(15)^2][5 (1735) -(85)^2]}[/tex]

[tex]r=0.00351[/tex]

The correlation coefficient is 0.00351