A researcher wants to determine the impact of soil type on the growth of a certa
ID: 3221362 • Letter: A
Question
A researcher wants to determine the impact of soil type on the growth of a certain type of plant. She grows three plants in each of four different types of soil and measures the growth in inches for each plant after one month resulting in the data below. Use this data: Assignment 9q2 data FOR R a) What null hypothesis is the researcher testing if she runs an ANOVA with this data? Soil 3 provides a lower mean growth for the plant than the other types of soil. The mean growth of the plant is different in each type of soil. The mean growth of the plant in each type of soil is the same. One type of soil has a higher mean growth for the plant than the others. The variability in growth of the plant in each type of soil is the same. b) What is the SS_trt for the ANOVA? Give your answer to at least three decimal places. __________ c) What is DF_err for the ANOVA? ______ d) What is the value of the F statistic for the ANOVA? Give your answer to at least three decimal places. _________ e) Using a 0.1 level of significance, what conclusion should the researcher reach? Soil 3 has a lower mean growth for the plant than the other types of soil. There is not enough evidence to reject the claim that the mean growth of the plant is the same in each type of soil. The mean growth of the plant is not the same for all soil types. Soil 1 has a higher mean growth for the plant than the other types of soil.Explanation / Answer
a) Correct Answer: Option (C)
b) SStreatment = 477
> readdata=read.table("E:/Assignment9q2.txt",header=TRUE, sep=",")
> inches=readdata$Inches
> soil=readdata$Soil
> y=c(inches,soil)
> n=rep(length(soil),2)
> group=rep(1:2,n)
> data=data.frame(y=y,group=factor(group))
> a1=aov(formula=y~group,data)
> a1
Call:
aov(formula = y ~ group, data = data)
Terms:
group Residuals
Sum of Squares 477.0417 42.1567
Deg. of Freedom 1 22
Residual standard error: 1.384273
Estimated effects may be unbalanced
> summary(a1)
Df Sum Sq Mean Sq F value Pr(>F)
group 1 477.0 477.0 248.9 1.77e-13 ***
Residuals 22 42.2 1.9
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
c) DF for error = 22
d) F-Statistic = 248.9
e) P=0.0000 which is less than alpha=0.1, we reject H0
Correct Answer: Option (C)
> readdata=read.table("E:/Assignment9q2.txt",header=TRUE, sep=",")
> inches=readdata$Inches
> soil=readdata$Soil
> y=c(inches,soil)
> n=rep(length(soil),2)
> group=rep(1:2,n)
> data=data.frame(y=y,group=factor(group))
> a1=aov(formula=y~group,data)
> a1
Call:
aov(formula = y ~ group, data = data)
Terms:
group Residuals
Sum of Squares 477.0417 42.1567
Deg. of Freedom 1 22
Residual standard error: 1.384273
Estimated effects may be unbalanced
> summary(a1)
Df Sum Sq Mean Sq F value Pr(>F)
group 1 477.0 477.0 248.9 1.77e-13 ***
Residuals 22 42.2 1.9
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
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