Three checkout lines at a supermarket use three different scanner systems that r

Question

Three checkout lines at a supermarket use three different scanner systems that read the UPC symbols on products and find the prices. The store manager suspects that the three scanner systems have different efficiencies and wants to check their speeds. He measures at randomly selected times the speed of each system in number of items scanned per minute. a. Fill the yellow blanks in the ANOVA table Anova: Single Factor SUMMARY Groups Count Sum Average Variance 14.4 2.044444 Scan 1 Scan 2 Scan 3 10 144 10 151 10 164 16.4 3.6 ANOVA Source of Variation P-value F crit 0.044887 3.354131 ss df MS 10.3 Factor Error Total 79.7 27 2.951852 100.3

Explanation / Answer

Ans:

First,complete the table:

SST=SSR+SSE

100.3=SSR+79.7

SSR=100.3-79.7=20.6

F=MSR/MSE=10.3/2.951852=3.489

p-value=Fdist(3.489,2,27)=0.044887

i)

H0:All three scanner systems have the same average number scanned per minute.

Ha:Atleast one of the scanner have different average number scanned per minute.

ii)Test statistic:

F=MSR/MSE=10.3/2.951852=3.489

iii)Decision rule:

F critical=Finv(0.05,2,27)=3.354

Reject null hypothesis,if Fstatistic>3.354

iv)Conclusion:

As,F=3.489>3.354,we reject null hypothesis.

(or p-value<0.05)

There is insufficient evidence to conclude that all three scanner systems have the same average number scanned per minute.

SS df MS F p-value F critical Factor 20.6 2 10.3 3.489 0.044887 3.354131 error 79.7 27 2.951852 Total 100.3 29

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