Problem 4 In Kocaoz, S. et al. (2005) a research is presented where two types of

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

Using R studio we can calculate the confidence intervals:

a) Code:

library(EnvStats)
A <- c(1015,991,1015,1029,955,1036,1031,992,975,944)
varTest(A,conf.level = 0.9)$conf.int

OUTPUT:

> library(EnvStats)
> A <- c(1015,991,1015,1029,955,1036,1031,992,975,944)
> varTest(A,conf.level = 0.9)$conf.int
LCL UCL
558.5503 2842.0389
attr(,"conf.level")
[1] 0.9

So, 90% confidence interval is (558.5503, 2842.0389).

b) CODE:

B <- c(963,973,945,1104,982,1027,1029,998,995,988)
t.test(B,conf.level = 0.95)$conf.int

OUTPUT:

> B <- c(963,973,945,1104,982,1027,1029,998,995,988)
> t.test(B,conf.level = 0.95)$conf.int
[1] 968.4044 1032.3956
attr(,"conf.level")
[1] 0.95

Here, 95% confidence interval is (968.4044, 1032.3956),

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