• R Problem: Suppose as a business manager you have the responsibility for testing and comparing the lifetimes of four brands (Apollo, Bridgestone, CEAT and Falken) of automobile tyres. The lifetime of these sample observations are measured in mileage run in ’000 miles. For each brand of automobile tyre, sample of 15 observations have been collected. On the basis of these information, you have to take your decision regarding the four brands of automobile tyre. The data is provided in the csv file format (called, tyre. csv).

Import the data into R from the link shared or alternatively see the attached excel document.

In addition use the following R commands to run it.

• model1<- aov(Mileage~Brands) • summary(model1)

• TukeyHSD(model1, conf. level = 0.95)

a) Identify the explanatory variable and response variable.

b) Identify the parameters of interest using correct notation.

c) Using α = 0.05, conduct ANOVA F-test to test whether at least two mean wait times are different. Conduct all five steps of ANOVA F-test, that is (i) check all necessary assumptions, (ii) state the null and alternative hypotheses, (iii) use summary(aov()) command to calculate F-test statistic and (iv) p-value, (v) draw the conclusion in the context of the problem. Include R output of summary(aov()) command in your Homework submission.

d) Based on your answer in part c) (v), do you think it is necessary to conduct Tukey’s Honest Significant multiple comparison? Explain.

e) Regardless of your answer from part e), use the output given below and interpret. If any two groups have statistically significant difference in their means, interpret the result.

Brands Mileage
Apollo 32.998
Apollo 36.435
Apollo 32.777
Apollo 37.637
Apollo 36.304
Apollo 35.915
Apollo 34.700
Apollo 32.379
Apollo 33.631
Apollo 36.419
Apollo 36.430
Apollo 34.836
Apollo 38.328
Apollo 30.623
Apollo 32.575
Bridgestone 33.523
Bridgestone 31.995
Bridgestone 35.006
Bridgestone 27.879
Bridgestone 31.297
Bridgestone 31.062
Bridgestone 34.838
Bridgestone 33.976
Bridgestone 32.552
Bridgestone 30.881
Bridgestone 28.144
Bridgestone 29.184
Bridgestone 33.075
Bridgestone 32.365
Bridgestone 30.925
CEAT 34.446
CEAT 32.807
CEAT 33.415
CEAT 36.861
CEAT 36.973
CEAT 35.081
CEAT 34.954
CEAT 33.475
CEAT 30.427
CEAT 36.134
CEAT 34.783
CEAT 36.117
CEAT 41.050
CEAT 32.168
CEAT 32.726
Falken 39.596
Falken 38.937
Falken 36.124
Falken 37.695
Falken 36.586
Falken 35.967
Falken 36.737
Falken 34.310
Falken 40.252
Falken 37.382
Falken 40.663
Falken 37.095
Falken 38.005
Falken 37.756
Falken 37.265