Question

In: Statistics and Probability

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

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.

Solutions

Expert Solution

  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.


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