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

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"† described an investigation of the intermolecular forces for UHPC connected to various substrates. The following work of adhesion measurements (in mJ/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.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 108 is a plausible value for the true average work of adhesion for UHPC adhered to steel?

The interval suggests that 108 is a possible value for the true average.The interval doesn't suggest that 108 is a possible value for the true average.   

Does the interval suggest that 111 is a plausible value for the true average work of adhesion for UHPC adhered to steel?

The interval suggests that 111 is a possible value for the true average.The interval doesn't suggest that 111 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).

The PI is wider than the CI.The CI is wider than the PI.    The two intervals are the same width.

(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/m2

Please Help With Part D, Thanks

Explanation / Answer

A)

Ho: data is normally distributed

H1: Data does not follow a normal distribution

Since the P value is greater than Alpha, 5%, I feel to reject the null hypothesis at 5% level of significance and conclude that the data is normally distributed.

B)

Mean= 107.78
sd= 1.075639345
n= 5
alpha= 0.05
t(a/2,n-1) t(0.05/2,5-1) 2.776

CI = mean +-t(a/2,n-1)*(sd/sqrt(n))
lower = 107.78-2.77644510519779*(1.07563934476199/sqrt(5))= 106.44
upper = 107.78 + 2.77644510519779*(1.07563934476199/sqrt(5))= 109.12

Since the confidence interval contains the value 108 I can say that "The interval suggests that 108 is a possible value for the true average."

Since the confidence interval does not contain the value 111, I can say that "The interval doesn't suggest that 111 is a possible value for the true average."

C)

Prediction interval

Mean +-t(A/2,n-1)*sd*sqrt(1+1/n)

Lower = 107.78-2.776445*1.075639*Sqrt(1+1/5) = 104.5085

Upper = 107.78 + 2.776445*1.075639*Sqrt(1+1/5) = 111.0515

Width of PI=6.543 > Width of CI= 2.6712

D)

At least 95% interval:

Mean +- tolerance critical value *s

lower = 107.78 - 5.079 ? 1.075639 = 102.3168

upper = 107.78 + 5.079 ? 1.075639 = 113.2432

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