We asked UST employees to tell us how many megabytes of memory (RAM) they have on their computer. We would like to test to see if the mean amount of memory is the same for three different academic departments. We have the memory amounts for six faculty members' machines in the three departments shown below. Dept. 1 Dept. 2 Dept. 3 1 2048 4096 4096 2 1024 2048 4096 3 1024 2048 8192 computer 4 2048 4096 8192 5 1024 2048 4096 6 2048 8192 2048 Here is the ANOVA table: Source DF Adj SS Adj MS F-Value P-Value Factor x 39263346 19631673 x.xx 0.025 Error xx 61691221 4112748 Total xx 100954567 After ANOVA, assume that we want to do all of the pairwise comparisons between the means and construct confidence interval estimates for the size of the difference between means. Tukey Pairwise Comparisons: Grouping Information Using the Tukey Method and 95% Confidence Factor N Mean Grouping dept 3 6 5120 A dept 2 6 3755 A B dept 1 6 1536 B Means that do not share a letter are significantly different. Construct a 95% confidence interval estimate for the difference between the mean for department 1 and the mean for department 2. Start by subtracting x bar 1 from x bar 2 to get a positive difference. You may use a t* multiplier of 2.13. Choose the interval here that matches most closely the interval you constructed. Answers: 1. 1990 to 5519 2. -820 to 5257 3. 546 to 6622 4. -1673 to 4404

We asked UST employees to tell us how many megabytes of memory (RAM) they have on their computer. We would like to test to see if the mean amount of memory is the same for three different academic departments. We have the memory amounts for six faculty members' machines in the three departments shown below. Dept. 1 Dept. 2 Dept. 3 1 2048 4096 4096 2 1024 2048 4096 3 1024 2048 8192 computer 4 2048 4096 8192 5 1024 2048 4096 6 2048 8192 2048 Here is the ANOVA table: Source DF Adj SS Adj MS F-Value P-Value Factor x 39263346 19631673 x.xx 0.025 Error xx 61691221 4112748 Total xx 100954567 After ANOVA, assume that we want to do all of the pairwise comparisons between the means and construct confidence interval estimates for the size of the difference between means. Tukey Pairwise Comparisons: Grouping Information Using the Tukey Method and 95% Confidence Factor N Mean Grouping dept 3 6 5120 A dept 2 6 3755 A B dept 1 6 1536 B Means that do not share a letter are significantly different. Construct a 95% confidence interval estimate for the difference between the mean for department 1 and the mean for department 2. Start by subtracting x bar 1 from x bar 2 to get a positive difference. You may use a t* multiplier of 2.13. Choose the interval here that matches most closely the interval you constructed. Answers: 1. 1990 to 5519 2. -820 to 5257 3. 546 to 6622 4. -1673 to 4404

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Dept. 1 Dept. 2 Dept. 3

1 2048 4096 4096

2 1024 2048 4096

3 1024 2048 8192

computer 4 2048 4096 8192

5 1024 2048 4096

6 2048 8192 2048

Here is the ANOVA table:

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	x	39263346	19631673	x.xx	0.025
Error	xx	61691221	4112748
Total	xx	100954567

After ANOVA, assume that we want to do all of the pairwise comparisons between the means and construct confidence interval estimates for the size of the difference between means.

Tukey Pairwise Comparisons: Grouping Information Using the Tukey Method and 95% Confidence

Factor	N	Mean	Grouping
dept 3	6	5120	A
dept 2	6	3755	A	B
dept 1	6	1536		B

Means that do not share a letter are significantly different.

Construct a 95% confidence interval estimate for the difference between the mean for department 1 and the mean for department 2. Start by subtracting x bar 1 from x bar 2 to get a positive difference. You may use a t* multiplier of 2.13. Choose the interval here that matches most closely the interval you constructed.

Answers:

1. 1990 to 5519

2. -820 to 5257

3. 546 to 6622

4. -1673 to 4404

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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