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Chapter 12: Q5CQQ (page 566)

Cola Weights The displayed results from Exercise 1 are from one-way analysis of variance. What is it about this test that characterizes it as one-way analysis of variance instead of two-way analysis of variance?

Short Answer

Expert verified

As the mean weights of the cans are categorized on only one factor, that is, the type of cola, the analysis of variance test is called the one-way analysis of variance test.

Step by step solution

01

Given information

An analysis of variance test is conducted to test the difference in the mean weights of the four samples of cola.

02

Describe the one-way and two-way analyses of variance

The term ‘factor’ refers to the independent variables of the study. Depending on the number of factors used to categorize the variable under study, the test for the comparison of three or more group means is referred to as a one-way or two-way analysis of variance.

  • In an analysis of variance test, if the sample values are categorized based on only one factor, it is called the one-way analysis of variance test.
  • In an analysis of variance test, if the sample values are categorized on two factors, it is called the two-way analysis of variance test.
  • The term ‘factor’ refers to the independent variables of the study. Depending on the number of factors used to categorize the variable under study, the test for the comparison of three or more group means is referred to as a one-way or two-way analysis of variance.
    • In an analysis of variance test, if the sample values are categorized based on only one factor, it is called the one-way analysis of variance test.
    • In an analysis of variance test, if the sample values are categorized on two factors, it is called the two-way analysis of variance test.

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Most popular questions from this chapter

Estimating Length Given below is a Minitab display resulting from two-way analysis of variance with sample data consisting of 18 different student visual estimates of the length of a classroom. The values are categorized according to sex and major (math, business, liberal arts). What do you conclude about an interaction between sex and major?

Weights The weights (kg) in the following table are from Data Set 1 “Body Data” in Appendix B. Results from two-way analysis of variance are also shown. Use the displayed results and use a 0.05 significance level. What do you conclude?


Female

Male

18-29

63.4

57.8

52.6

46.9

61.7

61.5

77.2

50.4

97

76.1

71.6

64.9

144.9

96.4

80.7

84.4

63.9

79

99.4

64.1

30-49

110.5

84.6

133.3

90.2

125.7

105.3

115.5

75.3

92.8

57.7

96.2

56.4

107.4

99.5

64.8

94.7

74.2

112.8

72.6

91.4

50-80

103.2

48.3

87.8

101.3

67.8

45.2

79.8

60.1

68.5

43.3

84.8

127.5

89.9

75.3

110.2

72.3

77.2

86.5

71.3

73.1

Flight Departure Delays Listed below are departure delay times (minutes) for American Airlines flights from New York to Los Angeles. Negative values correspond to flights that departed early. Use a 0.05 significance level to test the claim that the different flights have the same mean departure delay time. What notable feature of the data can be identified by visually examining the data?

Flight 1

-2

-1

-2

2

-2

0

-2

-3

Flight 19

19

-4

-5

-1

-4

73

0

1

Flight21

18

60

142

-1

-11

-1

47

13

Pancake Experiment Listed below are ratings of pancakes made by experts (based on data from Minitab). Different pancakes were made with and without a supplement and with different amounts of whey. The results from two-way analysis of variance are shown. Use the displayed results and a 0.05 significance level. What do you conclude?

Whey


0%

10%

20%

30%

No Supplement

4.4

4.5

4.3

4.6

4.5

4.8

4.5

4.8

4.8

4.6

4.7

5.1

Supplement

3.3

3.2

3.1

3.8

3.7

3.6

5.0

5.3

4.8

5.4

5.6

5.3

Confidence Interval Use the departure delay times for Flight 3 and construct a 95% confidence interval estimate of the population mean. Write a brief statement that interprets the confidence interval.
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