Question

In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance (to 2 decimals, if necessary). If the answer is zero enter "0". Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments 1,300 2 700 61.62 0.0 Error 500 44 11.36 Total 1,800 46 At a .05 level of significance, is there a significant difference between the treatments? The p-value is less than .01 What is your conclusion? Cannot conclude that the means of the three treatments are equal

          In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance (to 2 decimals, if necessary). If the answer is zero enter "0".
Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value
Treatments 1,300 2 700 61.62 0.0
Error 500 44 11.36
Total 1,800 46
At a .05 level of significance, is there a significant difference between the treatments?
The p-value is less than .01
What is your conclusion?
Cannot conclude that the means of the three treatments are equal

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In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance (to 2 decimals, if necessary). If the answer is zero enter "0".
Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value
Treatments 1,300 2 700 61.62 0.0
Error 500 44 11.36
Total 1,800 46
At a .05 level of significance, is there a significant difference between the treatments?
The p-value is less than .01
What is your conclusion?
Cannot conclude that the means of the three treatments are equal

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jacob Fry

04/17/2023

Step 1

We have the following information: - Treatments Sum of Squares (SST) = 1,300 - Error Sum of Squares (SSE) = 700 - Total Sum of Squares (SSTotal) = 1,800 - Degrees of Freedom for Treatments (dft) = 2 (since there are 3 treatments, dft = 3 - 1) - Show more…

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Completely randomized design, 12 experimental units were used for the first treatment; 15 for the second treatment; and 20 for the third treatment. Complete the following analysis of variance (to 2 decimals, if necessary). If the answer is zero, enter "0". Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square Treatments | 1,300 | 2 | 650.00 Error | 500 | 11 | 45.45 Total | 1,800 | 13 | - At a 0.05 level of significance, is there a significant difference between the treatments? The p-value is less than 0.01. What is your conclusion? We conclude that the means of the three treatments are significantly different.

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Transcript

00:01 So in this question we're filling out an anova table.

00:05 Let's see how many treatments we have.

00:09 So we have one, two, three treatments.

00:14 So three treatments means that the degrees of freedom for treatment is three minus one, so that's two.

00:23 So we can put a two in here straight away.

00:27 Now how many measurements do we make? 12 plus 15 plus 20.

00:32 So that gives 35 plus 12 is 47.

00:37 So 47 measurements means that the number of degrees of freedom in total is 47 minus one, which is 46.

00:49 But this is also equal to the number of degrees of freedom in the treatment plus the number of degrees of freedom in error.

00:57 So the degrees of freedom in error is the degrees of freedom in total minus the degrees of freedom in the treatment.

01:09 So that's 46 minus two, which is 44.

01:13 So we've got 44 in here, so the total degrees of freedom, 46.

01:19 Now the sum of squares in the treatment plus the sum of squares in the error is always equal to the sum of squares in total.

01:29 So we've got 1300 plus the sum of squares in the error is 1900.

01:36 So the sum of squares in the error is 600.

01:43 And now we can calculate the mean squares.

01:45 We have to remember that the mean square is always equal to the sum of squares divided by the degrees of freedom.

01:51 So here we've got 1300 over 2 is 650...

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