Ultra high performance concrete (UHPC) is a relatively new construction material
ID: 3151111 • 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 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 ic Point of View"t described an investigation of the 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.) 106.445 109.115 mJ/m2 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 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 o the experiment by calculating a 95% prediction interval. Round your answers to two decimal places. 104.51 111.05 mJ/m2 Compare the width of this interval to the width of the Cl from (b) The PI is wider than the Cl The two intervals are the same width. The Cl is wider than the PI 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. 106.45 X109.12Explanation / Answer
answer a) for small sample test it is assumed to parent population distribution is normal. so
it is plausible that distribution of sample could be normal
answer part 1 of b)
here n=5
this is small sample because its size is less than 30. so we use t-distribution and t-value for confidence interval
95%confidience interval for sample mean=mean±t(.05/2,n-1)*S/sqrt(n)=107.78 ± 2.7764*1.0756/sqrt(5)
=107.78 ± 1.3355=(106.445,109.115)
answer part 2 of b)
since 107 comes in the inverval of (106.445,109.115), so 107 is plausible value for ..........
answer part 3 of b)
since since 110 doesnot comes in the inverval of (106.445,109.115), so 110 is not plausible value for
answer part 4 of b)
95% prediction interval for sample mean=mean±t(.05/2,4)*S*sqrt(1+1/n)=107.78 ± 2.7764*1.0756*sqrt(1+1/5)
=107.78 ± 3.27=(104.51,111.05)
answer part 5 of b)
PI is wider than CI
answer part 6 of b)
99%confidience interval for sample mean=mean±t(.01/2,n-1)*S/sqrt(n)=107.78 ± 4.6*1.0756/sqrt(5)=
=107.78 ±2.21=(105.57,109.99)
x 107.1 109.5 107.4 106.8 108.1 mean= 107.78 S= 1.075639 t(.05,4)= 2.776445Related Questions
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