Question

Suppose that there are three different populations we want to compare, say P1, P2, and P3. Each of these populations is normal. A random sample from each population is taken, and the results are given below.

P1	P2	P3
10	6	5
12	8	9
9	3	12
15	0	8
13	2	4

a) Find the sample means and sample variance for each sample. Use Statistical Software and record the results in your Word document.
b) Combine all samples and find the mean of the data set with 15 data points. Call this the grand mean.
c) Use Statistical Software to create a graph that illustrates the sample means and the grand mean. Copy and paste your graph into your Word document.
d) Based on parts a, b, and c do the sample means appear to be approximately equal?

Using the data from this problem, use software to calculate F using the MSG and MSE.

Using the data from this problem, perform a one-way ANOVA test. Be sure to give the hypotheses, the value of F, the p-value, and the conclusion. Copy and paste the software output into your Word document.

Answer 1

using excel>data>data ananlysis>one way ANOVA

we have

ANOVA: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
P1	5	59	11.8	5.7000
P2	5	19	3.8	10.2000
P3	5	38	7.6	10.3000
	grand mean =	7.733333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	160.1333	2	80.0667	9.1679	0.0038	3.8853
Within Groups	104.8000	12	8.7333
Total	264.9333	14

a) the sample means and sample variance for each sample

Groups	Count	Sum	Average	Variance
P1	5	59	11.8	5.7000
P2	5	19	3.8	10.2000
P3	5	38	7.6	10.3000

b) Combine all samples and find the mean of the data set with 15 data points. the grand mean. is 7.73333
c)
dNO , sample means do not appear to be approximately equal

MSG = 80.0667 and MSE. = 8.7333

Ho : all means are equal

Ha: at least two means are different

t

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Groups	160.1333	2	80.0667	9.1679	0.0038	3.8853
Error	104.8000	12	8.7333
Total	264.9333	14

the value of F = 9.1679

, the p-value = 0.0038

the conclusion: since p value is less than 0.05 so we reject Ho and conclude thatat least two means are different