One way Analysis of Variance(ANOVA), F-test

Question

The data shows the result of experiment conducted to increase the sales of the company’s products,
where 3 strategies were utilized. Test whether there is significant difference among the 3 strategies
Based from the average sales/ day in million. α = 5%(0.05).
STRATEGIES
                                           A                       B                    C
                                           5                       6                     4
                                           9                       8                     6
                                          10                      7                    14
                                          14                      9                    10

 

Please help. Thanks.

Answer 1

A--------------------------------------------B-----------------------------------------C

5---------------------------------------------6-----------------------------------------4

9---------------------------------------------8-----------------------------------------6

10-------------------------------------------7----------------------------------------14

14-------------------------------------------9----------------------------------------10

38------------------------------------------30---------------------------------------34

μ_A=38/4 or 9.5-------------------μ_B=30/4 or 7.5------------------μ_C=34/4 or 8.5

μ_BAR=(38+30+34)/[4(3)] or 8.5

SSA is given by 4[(9.5-8.5)²+(7.5-8.5)²+(8.5-8.5)²] or 8.

SSE is given by (5-9.5)²+(9-9.5)²+(10-9.5)²+(14-9.5)²+(6-7.5)²+(8-7.5)²+(7-7.5)²+(9-7.5)²+(4-8.5)²+

(6-8.5)²+(14-8.5)²+(10-8.5)² or 105.

SST is given by SSA+SSE or 8+105 or 113.

VARIATION------SUM OF SQUARES-------DEGREES OF FREEDOM------MEAN SQUARE

Explained by------SSA=8------------------------------------------(3-1)=2-------------MSA=8/2 or 4

Strategies

(Between

Columns)

Error Or-----------SSE=105----------------------------------------(4-1)3=9------------MSE=105/9 or 35/3

Unexplained

(Within Columns)

Total---------------SST=(105+8)=113----------------------------4(3)-1=11

Obtain F Ratio from Table above as MSA/MSE or 4÷(35/3) or 12/35.

H₀: μ_A=μ_B=μ_C

H₁: μ_A≠μ_B≠μ_C

12/35 equivalent to 0.343 is less than F Tabular Value of 4.26 for 2 and 9 Degrees Of Freedom at 5% Significance Level (α=0.05) so one accepts the Null Hypothesis H₀ that the Mean Sales for each Strategy is the same.