Ultra high performance concrete (UHPC) is a relatively new construction material
ID: 2945977 • 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 m)/m2) for UHPC specimens adhered to steel appeared in the article. 107.1 109.5 107.4 106.8 108.1 (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/m2 Does the interval suggest that 109 is a plausible value for the true average work of adhesion for UHPC adhered to steel? O The interval suggests that 109 is a possible value for the true average O The interval doesn't suggest that 109 is a possible value for the true average. Does the interval suggest that 110 is a plausible value for the true average work of adhesion for UHPC adhered to steel? O The interval suggests that 110 is a possible value for the true average. The interval doesn't suggest that 110 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/m2 Compare the width of this interval to the width of the CI from (b) O The two intervals are the same width. The CI is wider than the PI O The PI is wider than the CIExplanation / Answer
R CODE included :
a) > samp=c(107.1,109.5,107.4,106.8,108.1)
> shapiro.test(samp)
Shapiro-Wilk normality test
data: samp
W = 0.8956, p-value = 0.386
Since p-value > 0.05, we accept the null hypothesis of normality assumption and conclude it is plausible that the distribution could be normal.
b)> t.test(samp)
One Sample t-test
data: samp
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
95% C.I : (106.4444,109.1156) m3/m2
The interval suggests that 109 is a possible value for the true average. (Since it is included in the C.I)
The interval does not suggest that 110 is a possible value for the true average.(Since it is not included in the C.I)
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