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.
 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  and the critical value would be:
 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
 groups and on each group from  we have
 we have  individuals on each group we can define the following formulas of variation:
 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.
 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  and the critical value would be:
 and the critical value would be: 
The confidence interval would be given by:

