10.63

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 livers 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 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 for this experiment are summarized in the following table and stored in CatFood.

一个宠物食品公司希望扩张它的产品线，现有产品是以肾脏和小虾为基础的猫粮。这家公司研发出两种新产品，一种基于鸡的肝脏，另一种基于鲜鱼。公司进行了一个实验来比较两种新产品和两种已有产品，以及另外一种在连锁超市销售的以牛肉为主要材料的同类产品。

对于这个实验，一个包含50 只当地动物收容所的猫的样本被选择出来。对要测试的5种产品都随机分配了 10只猫。每只猫都在喂食时间被提供3 盎司食物。研究者将变量定义为猫在 10 分钟内所吃掉的食物数量(从装满的盘子放到猫的面前开始计算)。这个实验的结果如下并存储在文件CatFood 中。

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

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

b. If appropriate, determine which products differ in the mean amount of food eaten?

c. At the 0.05 level of significance, is there evidence of a significant difference in the variation in the amount of food eaten among the various products?

d. What should the pet food company conclude? Fully describe the pet food company’s options with respect to the products.

a在0.05的显著性水平下，是否有证据表明不同产品被吃掉数量的均值存在差异?

b.如果有，确定哪些产品与其他产品被吃掉数量的均值存在显著差异。

c.在0.05的显著性水平下，是否有证据表明不同产品被吃掉数量的方差存在差异?

d.宠物食品公司应该得出什么结论? 根据这些产品描述公司会做出的选择。