Question

A pet food company has a business objective of expanding its product line beyond its current kidney and shrimp-based cat foods. The company developed two new products, one based on chicken liver and the other based on salmon. The company conducted an experiment to compare the two new products with its two existing ones, as well as a generic beef-based product sold at a supermarket chain. For the experiment, a sample of 50 cats from the population at a local animal shelter was selected. Ten cats were randomly assigned to each of the five products being tested. Each of the cats was then presented with 3 ounces of the selected food in a dish at feeding time. The researchers defined the variable to be measured as the number of ounces of food that the cat consumed within a 10-minute time interval that began when the filled dish was presented. The results are summarized in the dataset (CatFood.xlsx).

Where CatFood.xlsx Data:

Kidney Shrimp Chicken Liver Salmon Beef

2.37 2.26 2.29 1.79 2.09

2.62 2.69 2.23 2.33 1.87

2.31 2.25 2.41 1.96 1.67

2.47 2.45 2.68 2.05 1.64

2.59 2.34 2.25 2.26 2.16

2.62 2.37 2.17 2.24 1.75

2.34 2.22 2.37 1.96 1.18

2.47 2.56 2.26 1.58 1.92

2.45 2.36 2.45 2.18 1.32

2.32 2.59 2.57 1.93 1.94

To test that there is evidence of a difference in the mean amount of food eaten among the various products, fill in all the values in the following One-way ANOVA summary table.

Source of Variation	SS	df	MS	F
Among Groups
Within Groups				-
Total			-	-

At the 0.01 level of significance, is there evidence of a difference in the mean amount of food eaten among the various products? Test the hypothesis using F test based on the result of (a).

At the 0.01 level of significance, determine which products appear to differ significantly in the mean amount of food eaten using the Tukey-Kramer method.

At the 0.01 level of significance, is there evidence of a difference in the variation in the amount of food eaten among the various products? Test the homogeneity of the variances using the Levene’s test.

Answer 1

Excel Addon PHStat used

At the 0.01 level of significance, is there evidence of a difference in the mean amount of food eaten among the various products? Test the hypothesis using F test based on the result of (a).

ANOVA: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Kidney	10	24.56	2.456	0.0148
Shrimp	10	24.09	2.409	0.0253
Chicken Liver	10	23.68	2.368	0.0263
Salmon	10	20.28	2.028	0.0544
Beef	10	17.54	1.754	0.0990
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	3.6590	4	0.9147	20.8054	0.0000	3.7674
Within Groups	1.9785	45	0.0440
Total	5.6375	49
			Level of significance			0.01

Calculated F= 20.8054, P=0.0000 which is < 0.01 level of significance, Ho is rejected.

There is enough evidence of a difference in the mean amount of food eaten among the various products.

At the 0.01 level of significance, determine which products appear to differ significantly in the mean amount of food eaten using the Tukey-Kramer method.

Tukey-Kramer Multiple Comparisons
	Sample	Sample			Absolute	Std. Error	Critical
Group	Mean	Size		Comparison	Difference	of Difference	Range	Results
1: Kidney	2.456	10		Group 1 to Group 2	0.047	0.066307198	0.327	Means are not different
2: Shrimp	2.409	10		Group 1 to Group 3	0.088	0.066307198	0.327	Means are not different
3: Chicken Liver	2.368	10		Group 1 to Group 4	0.428	0.066307198	0.327	Means are different
4: Salmon	2.028	10		Group 1 to Group 5	0.702	0.066307198	0.327	Means are different
5: Beef	1.754	10		Group 2 to Group 3	0.041	0.066307198	0.327	Means are not different
				Group 2 to Group 4	0.381	0.066307198	0.327	Means are different
Other Data				Group 2 to Group 5	0.655	0.066307198	0.327	Means are different
Level of significance	0.01			Group 3 to Group 4	0.34	0.066307198	0.327	Means are different
Numerator d.f.	5			Group 3 to Group 5	0.614	0.066307198	0.327	Means are different
Denominator d.f.	45			Group 4 to Group 5	0.274	0.066307198	0.327	Means are not different
MSW	0.043966
Q Statistic	4.93

At the 0.01 level of significance, is there evidence of a difference in the variation in the amount of food eaten among the various products? Test the homogeneity of the variances using the Levene’s test.

ANOVA: Levene Test
SUMMARY
Groups	Count	Sum	Average	Variance
Kidney	10	0.98	0.098	0.0041
Shrimp	10	1.23	0.123	0.0107
Chicken Liver	10	1.28	0.128	0.0097
Salmon	10	1.84	0.184	0.0174
Beef	10	2.42	0.242	0.0374
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	0.1341	4	0.0335	2.1140	0.0947	3.7674
Within Groups	0.7137	45	0.0159
Total	0.8478	49
			Level of significance			0.01

Calculated F= 2.114, P=0.0947 which is > 0.01 level of significance, Ho is not rejected.

There is not enough evidence of a difference in the variation in the amount of food eaten among the various products.