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, 2 employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then 4 employees assembled them. They produced 25 during a one-hour period. The complete set of paired observations follows.

Number of Assemblers One Hour of Production (units)
2 15
4 25
1 10
5 40
3 30
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.

Answer 1

Answer:

(a) Shown below

(b) There is a positive relation between the number of assemblers and production.

(c) The correlation coefficient is 0.9272.

Step-by-step explanation:

Let X = number of assemblers and Y = number of units produced in an hour.

(a)

Consider the scatter plot below.

(b)

Based on the scatter plot it can be concluded that there is a positive relationship between the variables X and Y, i.e. as the value of X increases Y also increases.

(c)

The formula to compute the correlation coefficient is:

$r=\frac{n\sum XY-\sum X\sum Y}{\sqrt{[n\sum X^{2}-(\sum X)^{2}][n\sum Y^{2}-(\sum Y)^{2}]}} }$

Compute the correlation coefficient between X and Y as follows:

$r=\frac{n\sum XY-\sum X\sum Y}{\sqrt{[n\sum X^{2}-(\sum X)^{2}][n\sum Y^{2}-(\sum Y)^{2}]}} }=\frac{(5\times430)-(15\times120)}{\sqrt{[(5\times55)-15^{2}][(5\times3450)-120^{2}]}} =0.9272$

Thus, the correlation coefficient is 0.9272.