statistik

QUESTION

1. Sales, in hundreds of Ringgit Malaysia of cat food per day for the three shelf heights are as follows :

Shelf heightKnee level Waist level Eye level

77 88 8582 94 8586 93 8778 90 8181 91 80

Is there a significant difference in the average daily sales of this cat food based oh shelf height? Use a 0.01 level a significance.

ANSWER

Knee level Waist level Eye level Totalni 5 5 5 15 = nT i 404 456 418 1278 = T

1) Ʃx2 = 109284 , Ʃx = 1278 , n = 15

2) SST = Ʃ Ʃx2 – T2

n

= 109284 – (1278)2

15

= 398.40

3) SSB = ƩT12 – T2

n1 n

= ⦋T12 + T2

2 + T32 ⦌- T2

n1 n2 n3 n

= 404 2 + 4562 + 4182 – (1278)2

5 5 5 15

= 289.60

4) SSW = SST – SSB

= 398.40 – 289.60

= 108.80

5)

Source Sum of square Df Mean square FBetween 289.60 k – 1 = 3 – 1

= 2 ( v1)= 289.60 2= 144.80

= 144.80 9.07= 15.96

Within 108.80 n – k = 15 – 3 = 12 (v2)

= 108.80 12= 9.07

Total 398.40 n – 1 = 15 – 1 = 14

6) Hypothesis

H0 = µ1 = µ2 = µ3

H1 = atleast one mean are different

7) Significant level, α = 0.01

8) Test statistic

F = MSB

MSW

= 15.96

9) Critical region

Fα , v1 , v2 = F 0.01 , 2, 12 = 6.93 ( From table 9)

10) Decision rule

Reject H0 when F > Fα

Since F = 15.96 > Fα = 6.93, so reject H0

11) Conclusion

Atleast one mean are different