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 20The 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.
Accepted Solution
A:
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:[tex]r=\frac{n\sum XY-\sum X\sum Y}{\sqrt{[n\sum X^{2}-(\sum X)^{2}][n\sum Y^{2}-(\sum Y)^{2}]}} }[/tex]Compute the correlation coefficient between X and Y as follows: [tex]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[/tex]Thus, the correlation coefficient is 0.9272.