Suppose you are comparing four different delivery companies:A, B, C, Dand the times it takes to deliver a package within the Adelaide CBD. The data is collected by measuring the time taken over in 10 deliveries of each company.

Denote the mean delivery time of each company by

,

,

,

A

,

B

,

C

,

D

. You are interested to test the following hypothesis:

a)Assumptions were made when using ANOVA regarding the Normality of each company's sample and equal variances were assumed. Using the above Normality plots, comment on the validity of the model and check the assumption of equal variances.

(b)Perform a hypothesis test atto determine whether there is a difference between the mean delivery times.

(c)Using the output below (post Hoc) comparing the confidence intervals for the difference in means indicate which companies have similar and significantly different mean delivery times. Also, by using the output of the ANOVA test, explain which company appears to have on average the slowest delivery times compared to the other companies.

(d)Suppose the mean square error between the companies increases, how would this affect the F-statistic? What is the direction of change for the p-value? Explain.

One-way ANOVA: A, B, C, D Null hypothesis All means are equal Significance level = 0. 05 Equal variances were assumed for the analysis. Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Factor 3 73 . 44 24 . 480 5. 73 0 . 003 Error 36 153 . 68 4. 269 Total 39 227 .12 Model Summary S R-sq R-sq(adj) R-sq (pred) 2. 06614 32. 34% 26. 70% 16 . 46% Means Factor N Mean StDev 95% CI A 10 10 . 422 1 . 599 ( 9. 097, 11. 747) 10 11 . 594 1 . 550 (10.269, 12. 919) 10 13 . 015 2 . 545 (11 . 690, 14.340) 10 9. 375 2.375 ( 8. 050, 10. 700)Probability Plot of A Probability Plot of B Normal Normal Mean Mean 11.59 StDev 1.579 SIDev 1.550 10 10 15 AD 0.236 AD 0.377 P-Value 0.716 P-Value 0.317 70 60- Percent Percent 10 10 11 12 13 14 15 10 11 12 13 14 15 16 B Probability Plot of C Probability Plot of D Normal Normal 99 99 Mean 13:01 Mean 9.375 SWDev 2.545 StDev 2.375 10 15 N 10 AD 0.386 AD D.205 P-Value 0.319 p-Value 0.820 70 60 - ercent 50- Percent 20 10 - 10 12 14 16 18 20 5.0 7.5 10.0 12.5 15.0 D