# Hypothesis Testing For Anova Of Anova Essay

Introduction:

The case study deals with hypothesis testing in ANOVA. Where we have more than two samples. The samples are denoted by treatment also. We compare that whether the average effect of all the treatments is same or they differ significantly. Or we compare the independent mean and we conclude that whether the mean is same for all the populations or it differs significantly.

Case Study: We have picked 3 balls foam, whiffle and rubber. We threw all the balls 11 different times and noted the distance travelled by the ball. Now we have to test that whether any specific ball has the significant effect on the distance. Or all the balls are same. That means average effect of all the balls are same or whether it varies significantly. If the effect varies significantly then how it varies among different balls.

The data that has been noted down is as follows

Trial Foam Whiffle Rubber

1 123 109 119

2 120 111 117

3 118 109 116

4 120 108 114

5 119 107 116

6 120 110 115

7 120 113 113

8 122 109 113

9 121 108 109

10 117 108 113

11 120 108 116

Total 1320 1200 1261

Solution to the case study:

Now here we have 3 independent categorical variable or we have 3 treatments foam, whiffle and rubber. And we have one response variable called distance travelled.

Stating Hypothesis

Null Hypothesis, H0: µ1 = µ2 = µ3

That means we assume that average distance traveled by all the balls are same

Alternative Hypothesis, H1: µ1 ≠ µ2 ≠ µ3

That means average distance…