A pet food company has a business objective of expanding its product line beyond its current kidney and shrimp cat foods. The company conducted an experiment to compare its two existing products with three other products (chicken liver, salmon, and beef) 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. 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, which products appear to differ significantly in the mean amount of food eaten? c. What should the pet food company conclude? Fully describe the pet food company’s options with respect to the products.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A pet food company has a business objective of expanding its product line beyond its current kidney and shrimp cat foods. The company conducted an experiment to compare its two existing products with three other products (chicken liver, salmon, and beef) 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.

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, which products appear to differ significantly in the mean amount of food
eaten?
c. What should the pet food company conclude? Fully describe the pet food company’s options
with respect to the products.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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