In an era of increased awareness of the need for energy conservation, it is of i
ID: 3135137 • Letter: I
Question
In an era of increased awareness of the need for energy conservation, it is of interest to find out, when preparing a roast, what the consequences are of thawing a frozen roost before cooking and preheating the oven. The purpose of this 2 Times 4 factorial experiment is to provide some answers. The data are in the following table. The factors and levels are: Factor 1 (OVEN): level 1, not preheated (NOT PRE) level 2, preheated (PRE). Factor 2 (COND): level 1, fresh meat (ERESH) level 2,frozen meat (FROZEN) level 3, frozen, thawed for 12 h (12-THAW) level 4, frozen, thawed for 24 h (24- THAW). Starling with 40 roasts of the same size and configuration, five were randomly assigned to each of the eight factor level combinations. Each roust was crated until the internal temperature reached 160 degree F. The response is loud fuel requirement (GAS). It is required from you to Enter the data to R Define the factor levels Plot the profile plot. Implement the analysis of variance Locate the p-values Write the null and alternate hypotheses Compare the p-values with the 10% of significance level. Take a decision pertaining to the null hypothesis. Comment on the result in terms of the problem.Explanation / Answer
To enter data to R
1) Enter the data with the coloumn names into an Excel file and save it as "Book1.csv" .
2) In the R window, type: data<-read.csv("Book1.csv",header=T)
Defining the factor levels
The factor have 4 levels as mentioned in the problem:
Level1: fresh meat (FRESH)
Level2: frozen meat (FROZEN)
Level3: frozen, thawed for 12 hrs (12-THAW)
Level4: frozen, thawed for 24 hrs (24-THAW)
To perform the ANOVA
To perform the ANOVA, type in the following code in R:
> r = c(t(as.matrix(data)))
> f1<-c("fresh","frozen","x12.thaw","x24.thaw")
> k1=length(f1)
> n=10
> tm1 = gl(k1, 1, n*k1, factor(f1))
> av = aov(r ~ tm1 )
> summary(av)
This will give us the following ANOVA table
Df Sum Sq Mean Sq F value Pr(>F)
tm1 3 392.7 130.90 9.117 0.000127 ***
Residuals 36 516.9 14.36
The p-value is given to be 0.000127.
The null and alternative hypothesis
Null Hypotheses: the fuel requirement for cooking of all the four types of meat are same.
Alt Hypotheses: the fuel requirement for cooking of the four types of meat are not all same.
As the p-value = 0.000127<0.1 , we have enough evidence to reject the null hypothesis.
From the ANOVA result, we can say that- thawing a frozen roast does affect the cooking process.
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