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Ultra high performance concrete (UHPC) is a relatively new construction material

ID: 3060101 • Letter: U

Question

Ultra high performance concrete (UHPC) is a relatively new construction material that is characterized by strong adhesive properties with other materials. The article "Adhesive Power of Ultra High Performance Concrete from a Thermodynamic Point of View"t described an investigation of the intermolecular forces for UHPC connected to various substrates. The following work of adhesion measurements (in mJ/m) for UHPC specimens adhered to steel appeared in the article 107.1 109.5 107.4106.8 108.1 (a) Is it plausible that the given sample observations were selected from a normal distribution? It's plausible that the distribution could be normal O It's not plausible that the distribution could be normal (b) Calculate a two-sided 95% confidence interval for the true average work of adhesion for UHPC adhered to steel. (Round your answers to two decimal places.) mJ/m Does the interval suggest that 107 is a plausible value for the true average work of adhesion for UHPC adhered to steel? The interval suggests that 107 is a possible value for the true average O The interval doesn't suggest that 107 is a possible value for the true average Does the interval suggest that 112 is a plausible value for the true average work of adhesion for UHPC adhered to steel? O The interval suggests that 112 is a possible value for the true average The interval doesn't suggest that 112 is a possible value for the true average (c) Predict the resulting work of adhesion value resulting from a single future replication of the experiment by calculating a 95% prediction interval. (Round your answers to two decimal places.) mJ/m Compare the width of this interval to the width of the CI from (b) O The two intervals are the same width O The CI is wider than the PI The PI is wider than the CI. (d) Calculate an interval for which you can have a high degree of confidence that at least 95% of all UHPC specimens adhered to steel will have work of adhesion values between the limits of the interval. (Round your answers to two decimal places.) mJ/m You may need to use the appropriate table in the Appendix of Tables to answer this question

Explanation / Answer

Solutionb:

using R to create 95% Confidence inetrval

Run below code:

UHPC <- c(107.1,109.5,107.4,106.8,108.1)
t.test(UHPC)

Output:

One Sample t-test

data: UHPC

t = 224.06, df = 4, p-value = 2.38e-09

alternative hypothesis: true mean is not equal to 0

95 percent confidence interval:

106.4444 109.1156

sample estimates:

mean of x

107.78

Answer:

95% confidence interval for mean is

106.44,109.12

Solutionc:

df=n-1=5-1=4

alpha=0.05

t crit=2.776

sample mean =xbar=107.78

sample sd=s= 1.075639

95% Prediction interval PI is

xbar-t*s*sqrt(1+1/n),xbar+t*s*sqrt(1+1/n),

107.78-2.776*1.075639*sqrt(1+1/5),107.78+2.776*1.075639*sqrt(1+1/5)

104.51,111.05

answer is:

95% prediction interval for mean is

104.51,111.05

PI IS WIDER THAN CI

Solutiond:

95% confidence inetrvals are:

106.44,109.12