An engineer is interested in how the mean absorption of mois

An engineer is interested in how the mean absorption of moisture in concrete varies among 5 different concrete aggregates. The engineer decides to test six samples for each aggregate, requiring a total of 30 samples to be tested. The samples are exposed to moisture for 48 hours. A normal probability plot shows the samples from each aggregate come from a normal distribution and Bartlett’s test shows the standard deviations of all 5 groups are equal.

Suppose you do not have the data, but you are given the sum of squares between groups, sum of squares total and the p-value. Complete the ANOVA table below.

            ANOVA Table

Source of

Variation

Sum of

Squares

Degrees of

Freedom

Mean Square

(Variance)

F

Ratio

p-Value

Between Groups

(Factor/Treatment)

85356.47

0.00875

Within Groups

(Error)

Total

209376.80

Conduct a hypothesis test using all steps learned previously to determine if the mean absorptions differ between the five aggregates. Use level of significance.

Using the results from Tukey’s Pairwise Multiple Comparison test below, which aggregates are significantly different from each other?

Grouping Information Using Tukey Method

Agg N    Mean Grouping

5    6 610.67 A

3    6 610.50 A

2    6 569.33 A B

1    6 553.33 A B

4    6 465.17    B

Means that do not share a letter are significantly different.

Analysis of Variance is used to compare the means of 3 or more groups in order to control

_______________________ .

Analysis of Variance divides the variability of data into two parts. What are the two types of variability?

If the ratio of MS_B to MS_W is much greater than 1, this indicates _________________________________

______________________________________________

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square (Variance)	F Ratio	p-Value
Between Groups (Factor/Treatment)	85356.47				0.00875
Within Groups (Error)
Total	209376.80

Solution

Source of Variation

The null hypothesis will be that all population means are equal, the alternative hypothesis is that at least one mean is different. The p-value is less than the 5% or 1% level of significance,So, we reject the null hypothesis. We conclude that   the mean absorptions differ between the five aggregates.

Analysis of Variance is used to compare the means of 3 or more groups in order to control the average of the means of the two treatments

Analysis of Variance divides the variability of data into two parts. THe two typers of variability is

(1) within group variation (2) between group variation

The ratio MSB/MSW is a statistic that is approximately equal to 1 if the null hypothesis is true but when it will be larger than 1 if there are dierences between the population means.

Source of Variation	Sum of Square	Degreen of freedom	Mean Square	F-Ratio	P-value
Between group	85356.47	5	17071.29	3.303	0.00875
within group	124020.3	24	5167.514
Total	209376.80	29