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## Click on the Data button below to display the data. Copy the data into a statistical software package and click the Data button a second time to hide it. Data Guernsey Jersey Holstein 4.59 5.03 3.22 5.2 6.55 3.67 5.61 5.27 3.61 5.04 4.44 3.92 4.72 5.33 4.21 4.64 5.49 3.77 4.53 5.43 3.12 3.92 4.93 3.95 5.09 5.17 3.54 4.67 4.98 3.5 5.24 5.96 3.89 4.56 5.28 3.71 4.76 5.31 3.81 4.98 4.74 3.33 4.72 5.08 3.91 4.61 4.17 3.95 4.82 6.06   5.36 4.86   5.45     6.18     Choose the correct null and alternative hypotheses. H0: μ1=μ2=μ3H0: μ1=μ2=μ3 Ha: μ1,μ2,μ3Ha: μ1,μ2,μ3 are not all equal. Ha: μ1,μ2,μ3Ha: μ1,μ2,μ3 are not all equal. H0: μ1=μ2=μ3H0: μ1=μ2=μ3 H0: μ1=μ2=μ3H0: μ1=μ2=μ3 Ha: μ1≠μ2≠μ3Ha: μ1≠μ2≠μ3 H0: μ1≠μ2≠μ3H0: μ1≠μ2≠μ3 Ha: μ1=μ2=μ3Ha: μ1=μ2=μ3 Compute the test statistic. Compute the treatment sum of squares (SSTr) and the error sum of squares (SSE) and use them to complete the following ANOVA table. (Round your answers to 4 decimal places). Source S.S. df M.S. F Treatment         Error         Total         Compute the p-value. (Round your answer to 4 decimal places.) p-value =  Interpret the results of the significance test. The p-value provides strong evidence against the null hypothesis. The differences in the butterfat content of Guernsey, Holstein and Jersey cows is statistically significant. The p-value provides little evidence against the null hypothesis. The differences in the butterfat content of Guernsey, Holstein and Jersey cows is not statistically significant.

Background: The butterfat content of random samples of Guernsey, Holstein and Jersey cows are provided below. Each data value represents the percentage butterfat.

Directions: Perform an analysis of variance (ANOVA) to determine if the differences in the percentage butterfat of the different breeds of cows is statistically significant.

1. Click on the Data button below to display the data. Copy the data into a statistical software package and click the Data button a second time to hide it.

Data

Guernsey Jersey Holstein
4.59 5.03 3.22
5.2 6.55 3.67
5.61 5.27 3.61
5.04 4.44 3.92
4.72 5.33 4.21
4.64 5.49 3.77
4.53 5.43 3.12
3.92 4.93 3.95
5.09 5.17 3.54
4.67 4.98 3.5
5.24 5.96 3.89
4.56 5.28 3.71
4.76 5.31 3.81
4.98 4.74 3.33
4.72 5.08 3.91
4.61 4.17 3.95
4.82 6.06
5.36 4.86
5.45
6.18
2. Choose the correct null and alternative hypotheses.
• H0: μ1=μ2=μ3H0: μ1=μ2=μ3
Ha: μ1,μ2,μ3Ha: μ1,μ2,μ3 are not all equal.
• Ha: μ1,μ2,μ3Ha: μ1,μ2,μ3 are not all equal.
H0: μ1=μ2=μ3H0: μ1=μ2=μ3
• H0: μ1=μ2=μ3H0: μ1=μ2=μ3
Ha: μ1≠μ2≠μ3Ha: μ1≠μ2≠μ3
• H0: μ1≠μ2≠μ3H0: μ1≠μ2≠μ3
Ha: μ1=μ2=μ3Ha: μ1=μ2=μ3
3. Compute the test statistic.

Compute the treatment sum of squares (SSTr) and the error sum of squares (SSE) and use them to complete the following ANOVA table. (Round your answers to 4 decimal places).

 Source S.S. df M.S. F Treatment Error Total

p-value =

5. Interpret the results of the significance test.
• The p-value provides strong evidence against the null hypothesis. The differences in the butterfat content of Guernsey, Holstein and Jersey cows is statistically significant.
• The p-value provides little evidence against the null hypothesis. The differences in the butterfat content of Guernsey, Holstein and Jersey cows is not statistically significant.

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