Problem 4 In Kocaoz, S. et al. (2005) a research is presented where two types of
ID: 3370030 • Letter: P
Question
Problem 4 In Kocaoz, S. et al. (2005) a research is presented where two types of polymer bars are studied, whose tension is reinforced with fiberglass (FRP). These bars, replacing the steel beams, are used to reinforce concrete, so their characterization is important for design, control and optimization purposes for structural engineers. Two bars of this type were subjected to stress tests, the data obtained in Mpa, are shown below: Bars Resistance A | 1015 991 1015 1029 955 io36 1031 992 975 944 B 963 973 945 1104 982 1027 1029 998 995 988 a. Assuming a confidence level of 90%, what can be said about the voltage variability of type A bars? b. About average resistance of type B bars, what can be said considering a confidence level of 95%?Explanation / Answer
We have the R code to find the answer:
CODE:
a <- c(1015,991,1015,1029,955,1036,1031,992,975,944)
b <- c(963,973,945,1104,982,1027,1029,998,995,988)
df <- length(a) - 1
var <- var(a)
lower = var * df / qchisq(0.1/2, df, lower.tail = FALSE)
upper = var * df / qchisq(1 - 0.1/2, df, lower.tail = FALSE)
c(lower = lower, upper = upper)
t.test(b)$conf.int
OUTPUT:
> a <- c(1015,991,1015,1029,955,1036,1031,992,975,944)
> b <- c(963,973,945,1104,982,1027,1029,998,995,988)
> df <- length(a) - 1
> var <- var(a)
> lower = var * df / qchisq(0.1/2, df, lower.tail = FALSE)
> upper = var * df / qchisq(1 - 0.1/2, df, lower.tail = FALSE)
> c(lower = lower, upper = upper)
lower upper
558.5503 2842.0389
>
> t.test(b)$conf.int
[1] 968.4044 1032.3956
attr(,"conf.level")
[1] 0.95
a) Here the 90% confidence interval of the variance of bar A is (558.5503, 2842.0389).
So, we can say if we draw 100 samples from the population of bar A, 90 times the above interval include the true variance of bar A.
b) Here the 95% confidence interval of the average of bar B is (968.4044, 1032.3956)
So, we can say if we draw 100 samples from the population of bar B, 95 times the above interval include the true average of bar B.
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