Question

Suppose that there are three different populations we want to compare, say P₁, P₂ and P₃. Each of these populations are 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 Excel 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 Excel 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, 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.

Using the data from the first problem above, use the formulas given in the textbook to calculate F using the MSG and MSE.

Answer 1

1. Mean (p1)=11.8                Var(P1)=5.7

Mean(P2)= 3.8                   Var(P2)=10.2

Mean(P3)= 7.6                  Var(P3)=10.3

1. The samples are

10

12

9

15

13

6

8

3

0

2

5

9

12

8

4

Then Grand mean =7.7333            (by using Excel)

c) The graph is as follows:

  

1. The sample means are not so approximate.    

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
P1	5	59	11.8	5.7
P2	5	19	3.8	10.2
P3	5	38	7.6	10.3
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	160.1333	2	80.06667	9.167939	0.003831	3.885294
Within Groups	104.8	12	8.733333
Total	264.9333	14

Here p- value is 0.003831 is less than 0.05. Thus we reject H₀ as There is no significant effect of three samples.