Question

omework Check My Work oIn 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). Round p-value to four decimal places. If your answer is zero enter " Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments 1,000 Error 1,500 OTotal 1,500 At a.05 tevel of significance, is there a significant difference between the treatments The p-value is Select What is your conclusion? Select Check My Work Type here to search

Answer 1

Solution:

Given:
First Treatment: n1 = 12
Second Treatment: n2 = 15
Third Treatment: n3 = 20
SSTR = 1000
SST = 1500
We have to complete ANOVA table.

SSE = SST - SSTR

SSE = 1500 - 1000

SSE = 500

Degrees of Freedom:

df_treatments = k - 1

df_treatments = 3 - 1

df_treatments = 2

df_total = N - 1

where N = n1 + n2+ n3 = 12+15+20 = 47

Then

df_total = 47 - 1

df_total = 46

and

df_error =df_total - df_treatments

df_error = 46 - 2

df_error =44

Mean Squares:

MSTR = SSTR / df_treatment

MSTR = 1000 / 2

MSTR = 500

MSE = SSE / df_error

MSE = 500 / 44

MSE = 11.36

F = MSTR / MSE

F = 500 / 11.36

F = 44.00

P-value:

Use excel command:

=F.DIST.RT( x , df1 , df2 )

=F.DIST.RT( 44.00 , 2 , 44)

=0.0000

Thus p-value = 0.0000

ANOVA table
Source	SS	df	MS	F	p-value
Treatment	1,000	2	500.00	44.00	0.0000
Error	500	44	11.36
Total	1,500	46

At a 0.05 level of significance , is there a significant difference between the treatments?
The p-value is less than 0.05
Conclusion:
We reject H0, thus there is a significant difference between the treatments