Goochland Regional Bank has three branch offices in Goochland County, Virginia. The bank has a liberal sick leave policy, and a vice-president was concerned with employees taking advantage of this policy. She thought that the tendency to take advantage depended on the branch at which the employee worked. To see if there were differences in the mean time employees took for sick leave at the three branches, she asked each branch manager to sample employees randomly and record the number of days of sick leave taken last year. Fifteen employees were chosen, and the data are listed below. Do these data indicate a difference in mean sick leave days among the three branches? Use a level of significance level of 0.05. Be sure to show all six steps (including ANOVA table), to check assumptions, and (if appropriate) to use the Tukey-Kramer (Tukey’s W) procedure to determine which pairs of means are significantly different and which are similar (or explain why Tukey-Kramer is not appropriate). Please use SPSS ### Sick Leave Days Across Bank BranchesThis table presents the sick leave days taken by employees at three different bank branches. The data is organized to show the number of sick leave days taken during specific periods.#### Bank Branches and Sick Leave Data:- **MANAKIN** - Sick Leave Days: 2, 6, 8, 14, 14- **SANDY HOOK** - Sick Leave Days: 8, 10, 15, 17, 23- **GOOCHLAND CH** - Sick Leave Days: 4, 7, 8, 9, 15### Analysis:- **MANAKIN** shows a gradual increase in sick leave, peaking at 14 days.- **SANDY HOOK** demonstrates a steady increase, with the highest recorded at 23 days.- **GOOCHLAND CH** has moderate sick leave usage, reaching up to 15 days. This data can help in understanding patterns in sick leave usage and facilitating workforce management strategies.

The objective is to test whether the differences in mean time employees took for sick leave at the…

Answered: Goochland Regional Bank has three…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Goochland Regional Bank has three branch offices in Goochland County, Virginia. The bank has a liberal sick leave policy, and a vice-president was concerned with employees taking advantage of this policy. She thought that the tendency to take advantage depended on the branch at which the employee worked. To see if there were differences in the mean time employees took for sick leave at the three branches, she asked each branch manager to sample employees randomly and record the number of days of sick leave taken last year. Fifteen employees were chosen, and the data are listed below. Do these data indicate a difference in mean sick leave days among the three branches? Use a level of significance level of 0.05. Be sure to show all six steps (including ANOVA table), to check assumptions, and (if appropriate) to use the Tukey-Kramer (Tukey’s W) procedure to determine which pairs of means are significantly different and which are similar (or explain why Tukey-Kramer is not appropriate). Please use SPSS

### Sick Leave Days Across Bank Branches

This table presents the sick leave days taken by employees at three different bank branches. The data is organized to show the number of sick leave days taken during specific periods.

#### Bank Branches and Sick Leave Data:

- **MANAKIN**
- Sick Leave Days: 2, 6, 8, 14, 14

- **SANDY HOOK**
- Sick Leave Days: 8, 10, 15, 17, 23

- **GOOCHLAND CH**
- Sick Leave Days: 4, 7, 8, 9, 15

### Analysis:

- **MANAKIN** shows a gradual increase in sick leave, peaking at 14 days.
- **SANDY HOOK** demonstrates a steady increase, with the highest recorded at 23 days.
- **GOOCHLAND CH** has moderate sick leave usage, reaching up to 15 days.

This data can help in understanding patterns in sick leave usage and facilitating workforce management strategies.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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