Use the following scenario and data to answer the questions in this homework assignment.The local animal shelter has just learned that the dog food they have been using for years is no longer available. Because food is such an important aspect of the health and well-being of their dogs, they decide to test three different types of food. All three have the same nutritional value, but they may taste and smell different. To find out which food is preferred, each dog at the shelter is given three bowls of food with a different food in each. A volunteer times the how long each dog spends eating from the three bowls; the bowl with the most time is the "winner" for that dog and that food is marked as the preferred food. This is done for all 45 of the dogs in the shelterHere is the table of results that summarizes the food preferences of the dogs:

Meaty Max	Dog Chow One	Champs Choice
20	13	12

1. The director of the animal shelter wants to know if there is a significant difference in dog preference between these three food options. Why is it appropriate to use a Chi Square test for Goodness of Fit to answer this question? Explain your answer (1 point) 2. Given a sample of 45 dogs, if there is no preference between any of the three types of food (null hypothesis), what frequency count should we expect for each type? Insert your answers into the table below (.75 point)

Meaty Max	Dog Chow One	Champs Choice

In question 2, you identified the expected frequencies for the null hypothesis. The observed frequencies appear in the first table that shows the dogs' preferences. In questions 3 - 6, you will use those data to complete the Chi Square.Use this table to show your work when calculating the Chi Square

	Meaty Max	Dog Chow One	Champs Choice
Observed frequency (o)	20	13	12
Expected frequency (e)
(Subtract)
(Square)
(Divide)

(Sum) ²=Chi Square formula ²= 3. In the Chi Square formula you calculate a value for each of the conditions in the study. In that calculation you compare the observed and expected values to one another and then normalize them. The last step is to add the values from the three conditions together. First part of the Chi Square calculation where you find the values associated with each condition (final row in the table above). In other words, calculate (_o-_e)²/_efor each of the food conditions. Show your work to earn full credit (1 point)4. Complete the Chi Square calculation by summing the three values you obtained in Question 3 (1 point, show work to earn full credit) 5. What is thedffor this data set. (0.25 point)6. Assuming an alpha level = .05, what is the critical Chi-Square value for this data set? (Use the Chi-Square distribution table to answer this question; 0.5 point)7. Do the shelter dogs demonstrate a statistically significant difference in preference between these three food options? Explain your answer (0.5 point)