Question

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Limestone samples are taken from three different sections of the mine. Even through heating process is designed to reduce percent of silica in limestone, it may be possible that variation due to initial condition of raw limestone result in quality issues. (FYI: Number of samples for such test is usually in 100s to account for inner-regional variability) Conduct Bartlett's test of the following data to determine whether variances are equal at a = 0.01. Silica Content (%) Location A Location B Location C 0.78 1.69 1.41 0.10 060 0.65 1.48 2.65 0.15 0.27 1.82 2.68 1.51 0.19 1.56 061 1.94 0.68 2.89 0.13 0.79 1.38 2.44 0.84 2.09 1.57

Answer 1

we performe barttlet's test in   R SORTWARE

E4 D E F 1 A N m t in A B C BC 0.78 1.69 1.41 0.1 0.6 0.65 1.48 2.3 2.65 0.15 0.67 0.27 1.82 1.54 2.88 1.51 0.31 0.19 1.56 0.61 1.94 0.68 2.89 0.79 1.38 2.44 0.84 2.09 1.57 in 0.13

we performe barttlet's test in   R SORTWARE

code:

data= read.csv(file.choose(),header=T)
data
attach(data)
bartlett.test(list(data$A,data$B,data$C))

information about barttlet's test :

Bartlett’s test allows you to compare the variance of two or more samples to determine whether they are drawn from populations with equal variance. The test has the null hypothesis that the variances are equal and the alterntive hypothesis that they are not equal.

Ho : σ12 = σ22 = σ3 2 ,  all three sample variances are equal

H1:  at least two are different.

OUTPUT :

> bartlett.test(list(data$A,data$B,data$C))

   Bartlett test of homogeneity of variances

data: list(data$A, data$B, data$C)
Bartlett's K-squared = 2.6469, df = 2, p-value = 0.2662  

From the output we can see that the p-value of 0.2662 is not less than the significance level of 0.01. This means we cannot reject the null hypothesis that the variance is the same for all groups. This means that there is no evidence to suggest that the variance in limestone sample is different for the three sample groups.