A national pizza restaurant chain has developed 4 new pizzas.  Two are “meat lovers” pizzas and two are “cheese lovers” pizzas.  There is reason to believe that in total the meat lovers pizza’s will be liked better than cheese lovers pizzas.  

A test is set up with 4 groups, each containing 100 subjects.  Each subject is asked to evaluate on a scale from 1 (dislike greatly) to 10 (like greatly) how they rate the pizza.    Here are the results:

Group                        Mean

Meat Lovers 1           8.4

Meat Lovers 2           8.6

Cheese Lovers 1       6.9

Cheese Lovers 2       7.5

(It is OK to assume the standard errors are equal in all the groups.)  Each problem worth 10 points.

1. Fill out the following ANOVA table:

Source                     DF                Sum of Squares               Mean Square       F     P-Value

Model                   _____                        48                               ______          ___     ____

Error                    _____                      1584                              ______

Total                   _____                     _____                              ______

Pooled Standard Error ______

What is the null hypothesis and what conclusion can you make regarding the null hypothesis?

2. Given that we think the meat lovers pizzas in total will do better than the cheese lovers pizzas, write the formula for a suitable contrast.

What is the null and alternative hypothesis for testing the contrast?

What is the standard error of the contrast?

What is the value of the sample contrast?

What is it’s t-statistic, how many degrees of freedom does it have and what is the P-value of the t-statistic?

What conclusion can you make?