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, two employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then four employees assembled them. They produced 25 during a one-hour period. The complete set of paired observations follows. Number of Assemblers One-Hour 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. Click here for the Excel Data File Draw a scatter diagram. On the graph below, use the point tool to plot the point corresponding to the first Number of Assemblers and her Production (No of Assemblers1). Repeat the process for the remainder of the sample (No of Assemblers2, No of Assemblers3, … ). To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y. Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production? Compute the coefficient correlation. (Negative values should be indicated by a minus sign. Round sx, sy and r to 3 decimal places.) x y x−x¯x-x¯ y−y¯y-y¯ (x−x¯)2x-x¯2 (y−y¯)2y-y¯2 (x−x¯) (y−y¯)x-x¯ y-y¯ 2 15 −9 81 4 25 1 1 1 1 10 −14 196 5 40 2 4 32 3 30 6 0 0 x¯x¯ = y¯y¯ = Sx = Sy = r =
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, two employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then four employees assembled them. They produced 25 during a one-hour period. The complete set of paired observations follows.
| Number of Assemblers |
One-Hour 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.
Click here for the Excel Data File
-
Draw a
scatter diagram .
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On the graph below, use the point tool to plot the point corresponding to the first Number of Assemblers and her Production (No of Assemblers1).
-
Repeat the process for the remainder of the sample (No of Assemblers2, No of Assemblers3, … ).
-
To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.
-
Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production?
-
Compute the coefficient
correlation . (Negative values should be indicated by a minus sign. Round sx, sy and r to 3 decimal places.)
| x | y | x−x¯x-x¯ | y−y¯y-y¯ | (x−x¯)2x-x¯2 | (y−y¯)2y-y¯2 | (x−x¯) (y−y¯)x-x¯ y-y¯ |
| 2 | 15 | −9 | 81 | |||
| 4 | 25 | 1 | 1 | 1 | ||
| 1 | 10 | −14 | 196 | |||
| 5 | 40 | 2 | 4 | 32 | ||
| 3 | 30 | 6 | 0 | 0 | ||
| x¯x¯ | = | y¯y¯ | = | Sx | = |
| Sy | = | r | = |
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