Question

The following data are from a completely randomized design.

	Treatment	Treatment	Treatment
	A	B	C
	32	44	34
	30	43	37
	30	44	36
	26	46	37
	32	48	41
Sample mean	30	45	37
Sample variance	6	4	6.5

a. At the

level of significance, can we reject the null hypothesis that the means of the three treatments are equal?

Compute the values below (to 1 decimal, if necessary).

Sum of Squares, Treatment
Sum of Squares, Error
Mean Squares, Treatment
Mean Squares, Error

Calculate the value of the test statistic (to 2 decimals).

The -value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6

What is your conclusion?

- Select your answer -Conclude that not all treatment means are equalDo not reject the assumption that the treatment means are equalItem 7

b. Calculate the value of Fisher's LSD (to 2 decimals).

Use Fisher's LSD procedure to test whether there is a significant difference between the means for treatments A and B, treatments A and C, and treatments B and C. Use .

Difference	Absolute Value	Conclusion
		- Select your answer -Significant differenceNo significant differenceItem 10
		- Select your answer -Significant differenceNo significant differenceItem 12
		- Select your answer -Significant differenceNo significant differenceItem 14

c. Use Fisher's LSD procedure to develop a  confidence interval estimate of the difference between the means of treatments A and B (to 2 decimals). Since treatment B has the larger mean, the confidence interval for the difference between the means of treatments A and B ( ) should be reported with negative values.

(  ,   )

Answer 1

from above

a)

sum of sq;treatment=	676.00
sum of sq; error=	66.00
mean sq;treatment=	338.00
mean square; error=	4.40

test statistic =	76.82
p value is less than 0.01

-Conclude that not all treatment means are equal

b)

Fisher's (LSD) for group i and j =(tN-k)*(sp*√(1/ni+1/nj)   =

2.58

Difference	Absolute Value	Conclusion
x2-x1	15.00	significant difference
x3-x1	7.00	significant difference
x3-x2	8.00	significant difference

c)

			Lower bound	Upper bound
			(xi-xj)-ME	(xi-xj)+ME
μA-μB			-17.58	-12.42