Answer:
a) Null hypothesis:
Alternative hypothesis:
And we have this property
The degrees of freedom for the numerator on this case is given by where k =3 represent the number of groups.
The degrees of freedom for the denominator on this case is given by .
And the total degrees of freedom would be
The mean squares between groups are given by:
And the mean squares within are:
And the F statistic is given by:
And the p value is given by:
So then since the p value is lower then the significance level we have enough evidence to reject the null hypothesis and we conclude that we have at least on mean different between the 3 groups.
b)
The degrees of freedom are given by:
The confidence level is 99% so then and
and the critical value would be:
The confidence interval would be given by:
Step-by-step explanation:
Previous concepts
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"
Part a
Null hypothesis:
Alternative hypothesis:
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
The degrees of freedom for the numerator on this case is given by where k =3 represent the number of groups.
The degrees of freedom for the denominator on this case is given by .
And the total degrees of freedom would be
The mean squares between groups are given by:
And the mean squares within are:
And the F statistic is given by:
And the p value is given by:
So then since the p value is lower then the significance level we have enough evidence to reject the null hypothesis and we conclude that we have at least on mean different between the 3 groups.
Part b
For this case the confidence interval for the difference woud be given by:
The degrees of freedom are given by:
The confidence level is 99% so then and
and the critical value would be:
The confidence interval would be given by: