7. Folacin is the only B vitamin present in any significant amount in tea. Recen

Question

7. Folacin is the only B vitamin present in any significant amount in tea. Recent advances in assay methods have made accurate determination of folacin content feasible. Consider the accompanying data on folacin content for randomly selected specimens of the four leading brands of green tea. Does the data suggest that the true mean folacin content is the same for all brands? Execute a test at the = 0.05 level and make sure to fill in the ANOVA table with the proper values. Brand Observations

1) 8.0 6.3 6.7 8.7 9.0 10.2 11.6

2) 5.8 7.6 9.9 6.2 8.8

3) 6.9 7.6 5.1 7.5 5.4 5.0

4) 6.5 7.2 8.0 4.6 5.1 5.0

Parameters of interest:

Null H0:

Ha:

Decision:

Explanation / Answer

We shall analyse this in the open source statistical package R , the R snippet is as follows

one <- c(8.0, 6.3, 6.7, 8.7, 9.0, 10.2, 11.6)
two<- c(5.8 ,7.6 ,9.9, 6.2, 8.8)
three<- c(6.9, 7.6, 5.1, 7.5, 5.4, 5.0)
four <- c(6.5, 7.2, 8.0, 4.6, 5.1, 5.0)

data.df<- data.frame(cbind(one,two,three,four))

library(reshape2)
data.df<- melt(data.df)

a<- aov(lm(value~variable,data=data.df))

summary(a)

The anova table is

> summary(a)
Df Sum Sq Mean Sq F value Pr(>F)
variable 3 27.84 9.278 4.186 0.0162 * as the p value is less than 0.05 , thus the data suggests that the mean value is different across groups, atleast for 2 groups
Residuals 24 53.20 2.217   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

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