A pet food company conducted an experiment to compare five different cat foods.
ID: 3260477 • Letter: A
Question
A pet food company conducted an experiment to compare five different cat foods. A sample of 30 cats from the population at a local animal shelter was selected. Six cats were randomly assigned to each of the five products. Each 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. The results for this experiment are summarized in the accompanying table.
Kidney Shrimp Chicken_Liver Salmon Beef
2.38 2.25 2.29 1.79 1.74
2.61 2.69 2.24 1.83 1.52
2.31 2.26 2.41 1.96 1.19
2.48 2.46 2.68 2.05 1.63
2.59 2.34 2.25 2.26 1.68
2.61 2.36 2.58 1.58 1.32
Critical values of F. Cumulative Probabilities=0.95, Upper-Tail Areas=0.05.
Numerator, df 1
Denominator, df2 1 2 3 4 5 6 7 8 9 10
1 161.40 199.50 215.70 224.60 230.20 234.00 236.80 238.90 240.50 241.90
2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40
3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79
4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96
5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06
7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35
9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98
11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85
12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75
13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60
15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49
17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41
19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35
21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32
22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30
23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27
24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25
25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24
26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22
27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20
28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19
29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18
30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16
40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08
60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99
120 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96 1.91
infinity 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 1.83
Critical values of the Studentized Range, Q. Upper 5% points (alpha=0.05).
Numerator, df
Denominator, df 2 3 4 5 6 7 8 9 10
1 17.97 26.98 32.82 37.08 40.41 43.12 45.40 47.36 49.07
2 6.09 8.33 9.80 10.88 11.74 12.44 13.03 13.54 13.99
3 4.50 5.91 6.83 7.50 8.04 8.48 8.85 9.18 9.46
4 3.93 5.04 5.76 6.29 6.71 7.05 7.35 7.60 7.83
5 3.64 4.60 5.22 5.67 6.03 6.33 6.58 6.80 7.00
6 3.46 4.34 4.90 5.31 5.63 5.90 6.12 6.32 6.49
7 3.34 4.17 4.68 5.06 5.36 5.61 5.82 6.00 6.16
8 3.26 4.04 4.53 4.89 5.17 5.40 5.60 5.77 5.92
9 3.20 3.95 4.42 4.76 5.02 5.24 5.43 5.60 5.74
10 3.15 3.88 4.33 4.65 4.91 5.12 5.31 5.46 5.60
11 3.11 3.82 4.26 4.57 4.82 5.03 5.20 5.35 5.49
12 3.08 3.77 4.20 4.51 4.75 4.95 5.12 5.27 5.40
13 3.06 3.74 4.15 4.45 4.69 4.89 5.05 5.19 5.32
14 3.03 3.70 4.11 4.41 4.64 4.83 4.99 5.13 5.25
15 3.01 3.67 4.08 4.37 4.60 4.78 4.94 5.08 5.20
16 3.00 3.65 4.05 4.33 4.56 4.74 4.90 5.03 5.15
17 2.98 3.63 4.02 4.30 4.52 4.71 4.86 4.99 5.11
18 2.97 3.61 4.00 4.28 4.50 4.67 4.82 4.96 5.07
19 2.96 3.59 3.98 4.25 4.47 4.65 4.79 4.92 5.04
20 2.95 3.58 3.96 4.23 4.45 4.62 4.77 4.90 5.01
24 2.92 3.53 3.90 4.17 4.37 4.54 4.68 4.81 4.92
30 2.89 3.49 3.85 4.10 4.30 4.46 4.60 4.72 4.82
40 2.86 3.44 3.79 4.04 4.23 4.39 4.52 4.64 4.74
60 2.83 3.40 3.74 3.98 4.16 4.31 4.44 4.55 4.65
120 2.80 3.36 3.69 3.92 4.10 4.24 4.36 4.47 4.56
infinity 2.77 3.31 3.63 3.86 4.03 4.17 4.29 4.39 4.47
Complete (a) through (d) below.
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?
Determine the hypotheses. Choose the correct answer below.
A. H0: 1 = 2 = • • • = 55; H1: Not all jj are equal (where j = 1,2,...,55)
B. H0: 1 = 2 = • • • = 66; H1: Not all jj are equal (where =1,2,...,66)
C. H0: 1 = 2 = • • • = 55; H1: 1 2 • • • 55
D. H0: 1 = 2 = • • • = 66; H1: 1 2 • • • 66
Find the test statistic.
FSTAT = ____? (Round to two decimal places as needed.)
Determine the critical value.
= ____? (Round to two decimal places as needed.)
Reach a decision.
(Do not reject, Reject) H0. There is (sufficient, insufficient) 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.
Let the kidney-based cat food be group 1, the shrimp-based cat food be group 2, the chicken liver-based cat food be group 3, the salmon-based cat food be group 4, and the beef-based cat food be group 5.
Is there significant evidence that group 1 and group 2 differ in the mean amount of food eaten?
A. Yes
B. No
C. It is not appropriate to test which products differ in the mean amount of food eaten.
Is there significant evidence that group 1 and group 3 differ in the mean amount of food eaten?
A. Yes
B. No
C. It is not appropriate to test which products differ in the mean amount of food eaten.
Is there significant evidence that group 1 and group 4 differ in the mean amount of food eaten?
A. Yes
B. No
C. It is not appropriate to test which products differ in the mean amount of food eaten.
Is there significant evidence that group 1 and group 5 differ in the mean amount of food eaten?
A. Yes
B. No
C. It is not appropriate to test which products differ in the mean amount of food eaten.
Is there significant evidence that group 2 and group 3 differ in the mean amount of food eaten?
A. No
B. Yes
C. It is not appropriate to test which products differ in the mean amount of food eaten.
Is there significant evidence that group 2 and group 4 differ in the mean amount of food eaten?
A. No
B. Yes
C. It is not appropriate to test which products differ in the mean amount of food eaten.
Is there significant evidence that group 2 and group 5 differ in the mean amount of food eaten?
A. No
B. Yes
C. It is not appropriate to test which products differ in the mean amount of food eaten.
Is there significant evidence that group 3 and group 4 differ in the mean amount of food eaten?
A. No
B. Yes
C. It is not appropriate to test which products differ in the mean amount of food eaten.
Is there significant evidence that group 3 and group 5 differ in the mean amount of food eaten?
A. No
B. Yes
C. It is not appropriate to test which products differ in the mean amount of food eaten.
Is there significant evidence that group 4 and group 5 differ in the mean amount of food eaten?
A. No
B. Yes
C. It is not appropriate to test which products differ in the mean amount of food eaten.
c. At the 0.05 level of significance, is there evidence of a difference in the variation in the amount of food eaten among the various products?
Determine the hypotheses. Choose the correct answer below.
A. H0: 221 = 22 = • • • = 26; H1: Not all 2j are equal (where j =1,2,...,66)
B. H0: 21 = 22 = • • • = 25; H1: Not all 2j are equal (where j =1,2,...,55)
C. H0: 21 = 22 = • • • = 25; H1: 21 22 • • • 25
D. H0: 21 = 22 = • • • = 26; H1: 21 22 • • • 26
Find the test statistic.
FSTAT = ____? (Round to two decimal places as needed.)
Determine the critical value.
F = ____?(Round to two decimal places as needed.)
Reach a decision.
(Reject, Do not reject) H0. There is (sufficient, insufficient) evidence to conclude that there is a difference in the variation in the amount of food eaten among the various products.
d. The 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, which are the chicken liver- and salmon-based cat foods. The beef-based cat food is a generic product sold in a supermarket chain. What should the company conclude in terms of expanding its product line?
Choose the correct conclusion below.
A. The chicken liver-based cat food is the best choice for expansion. The salmon-based cat-food is a possibility for expansion; its mean amount of food eaten is significantly larger than the beef-based cat food, but smaller than the other cat foods.
B. The salmon-based cat food is the best choice for expansion. The chicken liver-based cat-food is a possibility for expansion; its mean amount of food eaten is significantly larger than the beef-based cat food, but smaller than the other cat foods.
C. It does not matter which product(s) is/are used for expansion because there are no significant differences in the mean amounts eaten among the various products
Explanation / Answer
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?
Determine the hypotheses. Choose the correct answer below.
correct ans is:
A. H0 : 1 = 2 = • • • = 55; H1 : Not all jj are equal (where j = 1,2, ...,55 )
Result of 1-WAY ANOVA test:
at 5% level, we reject H0 and conclude that there is a significant difference between at least one of the pairs of samples.
Anova: Single Factor SUMMARY Groups Count Sum Average Variance Kidney 6 14.98 2.496667 0.016627 Shrimp 6 14.36 2.393333 0.026947 Chicken_Liver 6 14.45 2.408333 0.034137 Salmon 6 11.47 1.911667 0.054857 Beef 6 9.08 1.513333 0.046947 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 4.24878 4 1.062195 29.58541 3.74E-09 2.75871 Within Groups 0.897567 25 0.035903 Total 5.146347 29Related Questions
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