Assumptions for the F test for comparing thre or more means Using the info below

Question

Assumptions for the F test for comparing thre or more means

Using the info below state the hypothesis, find the critical value, compare the test value, find the mean and variance for each sample, find the grand mean, find the between the group variance and find the within-group variance. Find the F test.

group 1: 420 570 636 377 258

group 2: 1006, 852, 1152, 1255, 1366

group 3: 880, 800, 508, 785, 702

1. State the hypothesis:

Hypotheses: Ho: µ1= µ2= µ3 (claim) H1: At least one mean is different from the others.

2. Find the critical values:

N = 15

k= 3

d.f.N.= k-1= 3-1=2

d.f.D.= N-k=15-3=12

3. Compute the test value:

a. mean and variance for each sample

b. grand mean:

c. netween-group variance:

d. within group variance:

e. find the F test:

Explanation / Answer

To solve this question we will do ANOVA using MS EXCEL.

3. Compute the test value:

a. mean and variance for each sample

Group 1: Mean = 452.2 Standard Deviation = 151.7109093

Group 2: Mean = 1126.2 Standard Deviation = 202.7269099

Group 3: Mean = 735 Standard Deviation = 141.7462522

b. grand mean: = 771.1333333

c. netween-group variance: SS(between) = 1145482.133

d. within group variance: = 336825.6

e. find the F test: = 20.40490034

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Standard Deviation Group 1 5 2261 452.2 23016.2 151.7109093 Group 2 5 5631 1126.2 41098.2 202.7269099 Group 3 5 3675 735 20092 141.7462522 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 1145482.133 2 572741.1 20.40490034 0.000137658 3.885293835 Within Groups 336825.6 12 28068.8 Total 1482307.733 14

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