A medical researcher is studying the effect of lidocaine on the enzyme level in the heart muscle of beagle dogs. Three different commercial brands of lidocaine (A), three dosage levels (B), and three dogs (C) are used in the experiment. Two replicates of a [tex]3^3[/tex] factorial design are run. The observed enzyme levels are as follows:

Replicate I:

- Dog 1
- Lidocaine Brand 1, Dosage 1: 96
- Lidocaine Brand 1, Dosage 2: 94
- Lidocaine Brand 1, Dosage 3: 101
- Lidocaine Brand 2, Dosage 1: 85
- Lidocaine Brand 2, Dosage 2: 95
- Lidocaine Brand 2, Dosage 3: 108
- Lidocaine Brand 3, Dosage 1: 84
- Lidocaine Brand 3, Dosage 2: 95
- Lidocaine Brand 3, Dosage 3: 105

- Dog 2
- Lidocaine Brand 1, Dosage 1: 84
- Lidocaine Brand 1, Dosage 2: 92
- Lidocaine Brand 1, Dosage 3: 102
- Lidocaine Brand 2, Dosage 1: 99
- Lidocaine Brand 2, Dosage 2: 106
- Lidocaine Brand 2, Dosage 3: 84
- Lidocaine Brand 3, Dosage 1: 98
- Lidocaine Brand 3, Dosage 2: 114
- Lidocaine Brand 3, Dosage 3: 83

- Dog 3
- Lidocaine Brand 1, Dosage 1: 97
- Lidocaine Brand 1, Dosage 2: 100
- Lidocaine Brand 1, Dosage 3: 86
- Lidocaine Brand 2, Dosage 1: 97
- Lidocaine Brand 2, Dosage 2: 109
- Lidocaine Brand 2, Dosage 3: 81
- Lidocaine Brand 3, Dosage 1: 93
- Lidocaine Brand 3, Dosage 2: 106
- Lidocaine Brand 3, Dosage 3: 79

Replicate II:

- Dog 1
- Lidocaine Brand 1, Dosage 1: 84
- Lidocaine Brand 1, Dosage 2: 85
- Lidocaine Brand 1, Dosage 3: 95
- Lidocaine Brand 2, Dosage 1: 97
- Lidocaine Brand 2, Dosage 2: 105
- Lidocaine Brand 2, Dosage 3: 104
- Lidocaine Brand 3, Dosage 1: 80
- Lidocaine Brand 3, Dosage 2: 82
- Lidocaine Brand 3, Dosage 3: 93

- Dog 2
- Lidocaine Brand 1, Dosage 1: 99
- Lidocaine Brand 1, Dosage 2: 110
- Lidocaine Brand 1, Dosage 3: 102
- Lidocaine Brand 2, Dosage 1: 83
- Lidocaine Brand 2, Dosage 2: 80
- Lidocaine Brand 2, Dosage 3: 96
- Lidocaine Brand 3, Dosage 1: 111
- Lidocaine Brand 3, Dosage 2: 85
- Lidocaine Brand 3, Dosage 3: 98

- Dog 3
- Lidocaine Brand 1, Dosage 1: 98
- Lidocaine Brand 1, Dosage 2: 86
- Lidocaine Brand 1, Dosage 3: 90
- Lidocaine Brand 2, Dosage 1: 103
- Lidocaine Brand 2, Dosage 2: 84
- Lidocaine Brand 2, Dosage 3: 95
- Lidocaine Brand 3, Dosage 1: 100
- Lidocaine Brand 3, Dosage 2: 79
- Lidocaine Brand 3, Dosage 3: 93

Task: Analyze the data from this experiment.

A 3³ factorial design with two replicates was conducted. The data will be analyzed to determine the main effects and interaction effects of the factors on the enzyme levels.

To analyze the data from this experiment, we will examine the main effects and interaction effects of the factors: lidocaine brand (A), dosage levels (B), and dogs (C). The enzyme levels observed in the two replicates will be analyzed to determine the significance of these factors.

First, we will calculate the average enzyme levels for each combination of factors (A, B, C). This will allow us to assess the main effects of the factors individually. We can then perform an analysis of variance (ANOVA) to determine if the main effects are statistically significant.

Next, we will investigate the interaction effects between the factors. This involves examining how the combination of factors (A, B, C) influences the enzyme levels. Interaction effects occur when the effects of one factor depend on the levels of another factor. We can assess these effects through ANOVA as well.

By analyzing the data using factorial analysis, we will be able to identify the significant factors and their effects on the enzyme levels in the heart muscle of beagle dogs. This information can provide insights into the impact of lidocaine brands and dosages on enzyme activity and help guide further research or medical decisions.

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