Question

8. A pet food company has a business objective of expanding its product line beyond its current kidney- and shrimp-based cat foots. 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 in supermarket chains.

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 5-minute period that began when the filled dish was presented to the cat. The results for this experiment are summarized in CatFood.

a. At the 0.05 level of significance, is there evidence of a differences in the mean amount of food eaten among the various products?

b. Does the result in (a) give you statistical permission to probe for individual differences between the food products?

Kidney	Shrimp	Chicken Liver	Salmon	Beef
3.00	0.25	2.61	0.63	2.97
3.00	0.34	3.00	1.37	2.85
1.47	0.16	3.00	3.00	0.44
2.62	0.72	2.43	0.54	0.90
1.51	3.00	3.00	3.00	3.00
3.00	3.00	3.00	2.55	3.00
3.00	0.29	2.85	2.93	0.48
3.00	3.00	0.18	2.73	0.45
0.74	1.99	0.98	3.00	3.00
2.21	2.30	1.51	0.96	0.05

Answer 1

a. At the 0.05 level of significance, is there evidence of a differences in the mean amount of food eaten among the various products?

The hypothesis being tested is:

H0: µ1 = µ2 = µ3 = µ4 = µ5

Ha: At least one means is not equal

	Mean	n	Std. Dev
	2.355	10	0.8351	Kidney
	1.505	10	1.2652	Shrimp
	2.256	10	1.0120	Chicken Liver
	2.071	10	1.0613	Salmon
	1.714	10	1.3335	Beef
	1.980	50	1.1181	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	5.2146	4	1.30366	1.05	.3938
Error	56.0413	45	1.24536
Total	61.2559	49

The p-value is 0.3938.

Since the p-value (0.3938) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is a difference in the mean amount of food eaten among the various products.

b. Does the result in (a) give you statistical permission to probe for individual differences between the food products?

No, because there is no difference in the mean amount of food eaten among the various products.

Please give me a thumbs-up if this helps you out. Thank you!