Statistics- A national pizza restaurant chain has developed 4 new pizzas

| March 29, 2017

Question
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?

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