Question

# In a completely randomized design, 12 experimental units were used for the first treatment, 15 for...

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 1,200 Error Total 1,800

At a .05 level of significance, is there a significant difference between the treatments?

The -value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 9

SOLUTION:

From given data,

12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment.

Error:

Sum of square for error = 1800 - 1200 =600

n= 12+15+20 = 47

Total degree of freedom=n-1=47-1= 46

treatments df = number of elements -1 = 3-1 =2

Error of df = 46-2 = 44

Mean square treatment = 1200 / 2 = 600

Mean square Error = 600 / 44 = 13.636

F = 600 / 13.636 = 44.001

numerator degree of freedom = 2

denominator degree of freedom =44

the p- value is 0.0000

Decision:

since p value is less than 0.05 significance level

we reject null hypothesis

Conclusion:

There is significant difference between treatments.

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