Two types A and B of solid fuel boilers are under investigation for the dust con
ID: 2945975 • Letter: T
Question
Two types A and B of solid fuel boilers are under investigation for the dust content of their flue gases. For this purpose 8 type A boilers and 6 type B boilers were used under identical fuelling and extraction conditions. Over the period of the investigation the following were the quantities in gm of dust deposited in similar traps in each of the 14 flues. A: 64, 75, 39, 47, 49, 81, 72, 61 B: 31, 57, 63, 40, 54, 49. Discuss the e Discuss the evidence for the foll : (a) Deposits are equally variable for the two types of boiler (b) The mean deposits for the two types are the same. Estimate the difference in the average amounts of dust deposited by the two types of boiler.Explanation / Answer
R code :
> dust=c(64,75,39,47,49,81,72,61,31,57,63,40,54,49)
> type=c(rep("A",8),rep("B",6))
> df=data.frame(dust,type)
> df
dust type
1 64 A
2 75 A
3 39 A
4 47 A
5 49 A
6 81 A
7 72 A
8 61 A
9 31 B
10 57 B
11 63 B
12 40 B
13 54 B
14 49 B
(a)#Bartlett's test for homogeneity of variance
> bartlett.test(dust~type,df)
Bartlett test of homogeneity of variances
data: dust by type
Bartlett's K-squared = 0.28985, df = 1, p-value = 0.5903
Since p-value > 0.05, we accept the null hypothesis of equal variance and conclude there is no significant difference in the variance of dust deposits for the two types.
(b)> summary(aov(dust~type,df))
Df Sum Sq Mean Sq F value Pr(>F)
type 1 493.7 493.7 2.645 0.13
Residuals 12 2240.0 186.7
Since p-value > 0.05, we accept the null hypothesis of equal variance and conclude there is no significant difference in the mean of dust deposits for the two types.
> attach(df)
The following objects are masked _by_ .GlobalEnv:
dust, type
> mean(dust[which(type=='A')])-mean(dust[which(type=='B')])
[1] 12 -> Estimate of difference in the average amounts of dust deposited by the two types
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