Question

Random sampling from four treatments produced the following data: Use Table 4.

Click here for the Excel Data File

Treatments
A	B	C	D
−11	−8	−8	−12
−13	−13	−13	−13
−10	−15	−8	−15
	−12	−13
		−10
X−AX−A = −11.3	X−BX−B = −12	X−CX−C = −10.4	X−DX−D = −13.3
sA2 = 2.33	sB2 = 8.7	sC2 = 6.3	sD2 = 2.3

a.	Calculate the grand mean. (Negative value should be indicated by a minus sign. Round your answer to 1 decimal place.)

Grand mean

b.	Calculate SSTR and MSTR. (Round intermediate values to 4 decimal places and final answers to 2 decimal places.)

SSTR
MSTR

c.	Calculate SSE and MSE. (Round intermediate values to 4 decimal places and final answers to 2 decimal places.)

SSE
MSE

d.	Specify the competing hypotheses in order to determine whether some differences exist between the population means.
	H0: μA ≥ μB ≥ μC; HA: Not all population means are equal. H0: μA ≤ μB ≤ μC; HA: Not all population means are equal. H0: μA = μB = μC; HA: Not all population means are equal.

e.	Calculate the value of the F test statistic. (Round your answer to 2 decimal places.)

F test statistic

f.	Approximate the p-value.
	p-value > 0.10 0.05 < p-value < 0.10 0.10 < p-value < 0.20 0.005 < p-value < 0.01

g.	At the 10% significance level, what is the conclusion to the test?
	Do not reject H0 Reject H0

Answer 1

Solution: We can use the excel ANOVA: Single Factor data analysis tool to find the answer to the given questions. The excel steps are given below:

Enter the data in excel as:

Click on Data > Data Analysis > ANOVA: Single Factor > OK

Input Range: Select all the data ranges here.

Mark the Labels

Alpha: 0.10

Press Ok. The excel output is given below:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	3	-34	-11.33	2.33
B	4	-48	-12.00	8.67
C	5	-52	-10.40	6.30
D	3	-40	-13.33	2.33
Grand Mean			-11.8
ANOVA
Source of Variation	SS	df	MS	F	P-value
Between Groups	17.07	3	5.69	1.03	0.415
Within Groups	60.53	11	5.50
Total	77.6	14

a. Calculate the grand mean.

Answer: