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. Draw a scatter diagram. Please state exact coordinates 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 =
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Exercise 13-4 (LO13-2)
| 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.
-
Draw a
scatter diagram . -
Please state exact coordinates
-
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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