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Analysis of the oil data set:

A project from Fall 1999 involved heating motor oil until it caught on fire. There were eight runs conducted in random order. Here, "conv" stands for conventional oil, "syn" stands for synthetic oil, "5/30" and "20/50" are two viscosities, and "time" is the time until catching fire. The data are as follows:

| Obs | Type | Viscosity | Time |
|-----|------|-----------|------|
| 1 | conv | 5/30 | 345 |
| 2 | syn | 5/30 | 658 |
| 3 | conv | 20/50 | 360 |
| 4 | syn | 20/50 | 546 |
| 5 | conv | 5/30 | 360 |
| 6 | syn | 5/30 | 676 |
| 7 | conv | 20/50 | 342 |
| 8 | syn | 20/50 | 512 |

Run a linear model (lm) in S-Plus or M-Lab to get the ANOVA output for determining if there is a mean difference in oil types (conv vs. syn). Use the full model: `model time = vis + type + vis*type`, after classifying vis and type.

Calculate the p-value to assess the mean difference in oil types.

Answer :

Answer:

See the explanation for the answer

Step-by-step explanation:

We shall analyse this in the open source statisitcal packageR , the complete R snippet is as follows


# read the data into R dataframe

data.df<- read.csv("C:\\Users\\586645\\Downloads\\Chegg\\syn.csv",header=TRUE)

str(data.df)



# perform anova analysis

a<- aov(lm(time~type*vis,data=data.df))


#summarise the results

summary(a)



colr<-c("salmon3" , "plum2","coral1","palegreen1" ,"orangered" ,"magenta4" )

# plots


boxplot(time~type*vis, data=data.df,ylab="Values",

main="Boxplots of the Data",col=colr,horizontal=TRUE)


attach(data.df)

interaction.plot(type,vis,time, type="b", col=c(2:6),

leg.bty="o", leg.bg="beige", lwd=2, pch=c(18,24,22),

xlab="Type",

ylab="Value",

main="Interaction Plot")


The results are


> summary(a)

Df Sum Sq Mean Sq F value Pr(>F)

type 1 121278 121278 478.18 2.59e-05 *** ### signficant as the p value is less than 0.05

vis 1 9730 9730 38.36 0.00345 ** ### signficant as the p value is less than 0.05

type:vis 1 9316 9316 36.73 0.00374 ** ### signficant as the p value is less than 0.05 , hence the interaction effect is significant . The p values are highlighted

Residuals 4 1015 254

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

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