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). Round p-value to four decimal places. If your answer is zero enter "0".

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments	1,300
Error
Total	2,000

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

The p-value is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 9

What is your conclusion?
SelectConclude not all treatment means are equalCannot reject the assumption all treatment means are equal

Answer 1

Answer:

From given information

The sum of squares for error is

SSE = SST-SSTR

SSE = 2000-1300

SSE = 700

Degree of freedom:

Here

N = 12+15+20

N = 47

df(treatment) = k-1

df(treatment) = 3-1

df(treatment) = 2

df(total) = N -1

df(total) = 47-1

df(total) = 46

df(error) = N - K

df(error) = 47-3

df(error) = 44

Now to find the mean square error:

MSE = SSE /N-k

MSE = 700/ 47-3

MSE = 700/ 44

MSE = 15.909

Therefore the mean squrae error is 15.909

Now to find the mean square treatment:

MSTR = SSTR/(k-1)

MSTR = 1300/(3-1)

MSTR = 1300/2

MSTR = 650

Therefore the mean square treatment is 650

Now to find the F- statistic:

F- statistic = MSTR / MSE

F- statistic = 650/ 15.909

F- statistic = 40.8574

Therefore the value of F- statistic is 40.8574

Now to find the P- Value:

P- value = 0.0000

Source of Variations	Sum of Squares	Degrees of freedom	Mean square	F	P- Value
Treatment	1300	2	650	40.8574	0.0000
Error	700	44	15.909
Total	2000	46

The P- Value is less than 0.01

Decision:

P -Value <

0.0000 < 0.05

Since the P -Value is less than significance level.Therefore we reject the null hypothesis(H0) at 0.05 level of significance.

Conclusion:

Conclude not all treatment means are equal.