The following data are from a completely randomized design:

Treatment
A: 162, 141, 167, 145, 149, 172
B: 147, 156, 129, 147, 139, 134
C: 124, 122, 139, 141, 152, 138

Sample mean: A = 156, B = 142, C = 136
Sample variance: A = 161.6, B = 97.6, C = 126.8

a. Compute the sum of squares between treatments (to the nearest whole number).
b. Compute the mean square between treatments (to 1 decimal).
c. Compute the sum of squares due to error (to the nearest whole number).
d. Compute the mean square due to error (to 1 decimal).
e. Set up the ANOVA table for this problem. Round all Sum of Squares to the nearest whole numbers. Round all Mean Squares to one decimal place. Round F to two decimal places. Round your p-value to four decimal places.

Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value
---|---|---|---|---|---
Treatments | | | | |
Error | | | | |
Total | | | | |

f. At the 0.05 level of significance, test whether the means for the three treatments are equal.
Calculate the value of the test statistic (to 1 decimal).
The p-value is:
- less than 0.01
- between 0.01 and 0.025
- between 0.025 and 0.05
- between 0.05 and 0.10
- greater than 0.10

What is your conclusion?
- Conclude that not all treatment means are equal
- Do not reject the assumption that the means for all three treatments are equal

You need to calculate several statistical parameters from the provided treatment data, set up an ANOVA table, and carry out a test to determine whether the means of the treatments are equal or not.

Explanation:

The question is looking for the calculation of several statistical values from given treatment data. These values include the sum of squares between treatments, mean square between treatments, sum of squares due to error, and mean square due to error.

ANOVA (Analysis of Variance) table will be setup and statistical test will be carried out to determine if the means of the treatments are equal or not.

For calculation of the sum of squares (SS) between the treatments, you need to subtract each sample mean from the grand mean, square the results, and then sum them up.

Mean square (MS) is calculated by dividing the SS by its corresponding degrees of freedom. SS Error is obtained by adding the variances of each treatment multiplied by their corresponding degrees of freedom. MS Error is computed by dividing SS Error by its corresponding degrees of freedom.

The ANOVA table will comprise of the Source of Variation (Treatments, Error, and Total), their respective sums of squares, degrees of freedom, mean squares and their F and p-values. The test statistic is obtained by dividing the MS Between by the MS Within.

Once the p-value is obtained, it can be compared with the given significance level to conclude if the means of the treatments are different or not.

If p-value is less than the significance level, the null hypothesis that states the means are equal is rejected indicating that at least one of the means is different.

Learn more about statistical parameters

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