To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained.
Machine	Hours
Machine 1	6.7
Machine 1	7.9
Machine 1	5.5
Machine 1	7.5
Machine 1	8.6
Machine 1	7.6
Machine 2	8.8
Machine 2	7.7
Machine 2	9.7
Machine 2	10.2
Machine 2	9.3
Machine 2	10.1
Machine 3	10.9
Machine 3	10.2
Machine 3	9.7
Machine 3	10.2
Machine 3	9.0
Machine 3	8.8
Machine 4	9.8
Machine 4	12.7
Machine 4	12.0
Machine 4	10.6
Machine 4	11.2
Machine 4	11.5
Use Fisher's LSD and the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experimentwise error rate of 0.05 is desired.
Find the comparisonwise error rate. (Round your answer to 4 decimal places.)
𝛼 =
0.0083

Correct: Your answer is correct.
Find the p-value for the hypothesis test for the difference between means for each pair of machines.
H0: 𝜇1 = 𝜇2
Ha: 𝜇1 ≠ 𝜇2
,   	p-value =

H0: 𝜇1 = 𝜇3
Ha: 𝜇1 ≠ 𝜇3
,   	p-value =

H0: 𝜇1 = 𝜇4
Ha: 𝜇1 ≠ 𝜇4
,   	p-value =
0.00

H0: 𝜇2 = 𝜇3
Ha: 𝜇2 ≠ 𝜇3
,   	p-value =

H0: 𝜇2 = 𝜇4
Ha: 𝜇2 ≠ 𝜇4
,   	p-value =

H0: 𝜇3 = 𝜇4
Ha: 𝜇3 ≠ 𝜇4
,   	p-value =

To perform hypothesis tests for the difference between means of machines using Fisher's LSD (Least Significant Difference) method, we will proceed in several steps. Let's outline the necessary steps:

### 1. **Compute the Means for Each Machine Group**

We first need to calculate the sample means of the four machines based on the data provided.

For **Machine 1**:
\[
\text{Mean of Machine 1} = \frac{6.7 + 7.9 + 5.5 + 7.5 + 8.6 + 7.6}{6}
\]
For **Machine 2**:
\[
\text{Mean of Machine 2} = \frac{8.8 + 7.7 + 9.7 + 10.2 + 9.3 + 10.1}{6}
\]
For **Machine 3**:
\[
\text{Mean of Machine 3} = \frac{10.9 + 10.2 + 9.7 + 10.2 + 9.0 + 8.8}{6}
\]
For **Machine 4**:
\[
\text{Mean of Machine 4} = \frac{9.8 + 12.7 + 12.0 + 10.6 + 11.2 + 11.5}{6}
\]

I'll compute these means now.The means for each machine are:

- **Machine 1**: 7.3000
- **Machine 2**: 9.3000
- **Machine 3**: 9.8000
- **Machine 4**: 11.3000

### 2. **Calculate the Mean Square Error (MSE)**

The Mean Square Error (MSE) is needed for Fisher's LSD test. To compute the MSE, we need to determine the variance within the groups. This involves:

- Finding the residual sum of squares (SSW), and
- Dividing by the degrees of freedom (df = total number of observations - number of groups).

Next, I'll calculate the MSE for this data set.

To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained. Use Fisher's LSD and the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experimentwise error rate of 0.05 is desired. Find the comparisonwise error rate and p-values for hypothesis tests for the difference between means for each pair of machines.

Explore how to use Fisher's LSD and Bonferroni adjustment to test for significant differences in machine breakdown times. This analysis includes hypothesis testing between all pairs of machines, detailed calculation of p-values, and the use of an experimentwise error rate of 0.05.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation