Solution :
We know that 

 At least one mean is different form the others (claim)
 At least one mean is different form the others (claim)
We need to find the critical values. 
We know k = 3 , N = 35, α = 0.05
d.f.N = k - 1
        = 3 - 1 = 2
d.f.D = N - k
         = 35 - 3 = 32
SO the critical value is 3.295
The mean and the variance of each sample :
Goust                      Jet red                 Cloudtran
 
            
        
 
       
         
The grand mean or the overall mean is(GM) :

          
         = 52.1714
The variance between the groups

      ![$=\frac{\left[14(50.5-52.1714)^2+14(52.07143-52.1714)^2+7(55.71426-52.1714)^2\right]}{3-1}$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B%5Cleft%5B14%2850.5-52.1714%29%5E2%2B14%2852.07143-52.1714%29%5E2%2B7%2855.71426-52.1714%29%5E2%5Cright%5D%7D%7B3-1%7D%24)
    
    = 63.55714
The Variance within the groups 
 
     
    
   = 20.93304
The F-test  statistics value is :

   
   = 3.036212
Now since the 3.036 < 3.295, we do not reject the null hypothesis.
So there is no sufficient evidence to support the claim that there is a difference among the means.
The ANOVA table is :
Source       Sum of squares    d.f    Mean square    F
Between    127.1143                 2      63.55714          3.036212
Within        669.8571             32      20.93304
Total           796.9714            34