As part of an evaluation program, a sporting goods retailer wanted to compare th
ID: 3217211 • Letter: A
Question
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below. Referring Table 11-6, based on the Tukey-Kramer the procedure with an overall level of significance of 0.05, the retailer would decide that the mean speed for the the brand is significantly different from each of the mean speeds for other brands. Show work.Explanation / Answer
The r code for the above problem is given as follows:
data<-c(43,46,43,37,38,39,41,45,42,43,45,46)
trial<-rep(c("1","2","3"),4)
persons<-c(rep("Barth",3),rep("Tornado",3),rep("Reiser",3),rep("Shaw",3))
df<-data.frame(data,trial,persons)
df
df.aov<-aov(data~trial+persons,data=df)
df.aov
summary(df.aov)
TukeyHSD(df.aov)
OUTPUT:
df.aov<-aov(data~trial+persons,data=df)
> df.aov
Call:
aov(formula = data ~ trial + persons, data = df)
Terms:
trial persons Residuals
Sum of Squares 12.66667 81.33333 8.66667
Deg. of Freedom 2 3 6
Residual standard error: 1.20185
Estimated effects may be unbalanced
> summary(df.aov)
Df Sum Sq Mean Sq F value Pr(>F)
trial 2 12.67 6.333 4.385 0.06705 .
persons 3 81.33 27.111 18.769 0.00188 **
Residuals 6 8.67 1.444
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> TukeyHSD(df.aov)
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = data ~ trial + persons, data = df)
$trial
diff lwr upr p adj
2-1 2.5 -0.1075319 5.107532 0.0584768
3-1 1.5 -1.1075319 4.107532 0.2586708
3-2 -1.0 -3.6075319 1.607532 0.5074977
$persons
diff lwr upr p adj
Reiser-Barth -1.3333333 -4.730334 2.063667 0.5638847
Shaw-Barth 0.6666667 -2.730334 4.063667 0.9012861
Tornado-Barth -6.0000000 -9.397001 -2.602999 0.0035473
Shaw-Reiser 2.0000000 -1.397001 5.397001 0.2726170
Tornado-Reiser -4.6666667 -8.063667 -1.269666 0.0123942
Tornado-Shaw -6.6666667 -10.063667 -3.269666 0.0020398
Therefore, it can be said that the mean speed of Tornado is significantly different from each of the mean speeds for other brands.
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