5. In recent years, lack of confidence in the Postal Service has led many compan

Question

5. In recent years, lack of confidence in the Postal Service has led many companies to send all by private courier. A large company is in the process of selecting one of three delivery method. To help in making the decision, an experiment of the three couriers. Because the company is concerned that the time of day may affect the delivery and they want to was performed whereby leters were sent using eaclh number of minutes required for delivery was recorded. Use the partially completed ANOVA table below to perfonm the required tests. 20023 %333 6.35, .00061.000 3 19 174 54000 39 000 3 181 60.333 9333 199 333 1433 205 m, 25 m 11060 7000 3 117 314333 213 71.000 1.000 206 68se, sam 12 814 7833 7 424 Couner 1 Counier 2 12 78 64833 5161 1150 222 Time af Dv 95 118 Perform the necessary tests to detemine () if blocking was necessary, (2) if there is a difference in couriers, and significance level of 0.05S. (30 points) are differences, determine where the differences are (i.e. Can you name a best courier?).Use a BLOCKING TEST State the Null and Alternative Hypotheses of Interest The critical value of the test statistic for alpha-0.05 is The calculated value of the test statistic is: Conclusion:

Explanation / Answer

the complete anova is given as

courier SS=(total)SS- total of time (SS) - error SS=1849.556-1150.222-495.111=204.2227

MS=SS/df

F=MS/MS(error)

(1) yes blocking was necessary as its effect is significant

(2) yes, there is difference in courier as its F-value is more than corresponding critical value of F

(3) LSD=sqrt(2*mse/r)*t(alpha,error df)=sqrt(2*22.51/12)*t(0.05,22)=sqrt(2*22.51/12)*2.07=4.01

so difference (67.833-62.000=5.833>LSD=4.01) between mean of courier1 and courier3 is significant

other pair courier 1 & courier 2 and courier 2 & 3 are not significant

blocking effect

null hypotheis H0: all blocking effect are same

alternate hypothesis : atleast one blocking effect is different from another

critical value=F(0.05,11,22)=2.26

calculated F=104.57/22.51=4.65

reject H0 as caculated F is more than critica F and concluded that there is effect of blocking

source SS df MS F Fcritical time of day 1150.222 11 104.5657 4.64632 2.258518 courier 204.2227 2 102.1111 4.537253 3.443357 error 495.1111 22 22.50505 total 1849.556 35

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