Answer:
For this case after conduct the ANOVA procedure they got an statistic of:
With a p value of :
Since the p value is lower than the significance level
We can reject the null hypothesis that the means are equal at the significance level provided.
For school 1 and 2 we have:
For school 1 and 3
For school 2 and 3 we have:
So as we can see we have significant difference between the means of school 1 and 3, and school 2 and 3
Step-by-step explanation:
Previous concetps
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
Solution to the problem
The hypothesis for this case are:
Null hypothesis:
Alternative hypothesis: Not all the means are equal
If we assume that we have groups and on each group from
we have
individuals on each group we can define the following formulas of variation:
And we have this property
For this case after conduct the ANOVA procedure they got an statistic of:
With a p value of :
Since the p value is lower than the significance level
We can reject the null hypothesis that the means are equal at the significance level provided.
For the other part we can calculate the 3 statistics with the following formula:
For school 1 and 2 we have:
For school 1 and 3
For school 2 and 3 we have:
So as we can see we have significant difference between the means of school 1 and 3, and school 2 and 3