4. (20 pts) A civil engineer is analyzing the compressive strength of concrete. It is known that the compressive strengt

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4 20 Pts A Civil Engineer Is Analyzing The Compressive Strength Of Concrete It Is Known That The Compressive Strengt 1 (72.51 KiB) Viewed 18 times

4. (20 pts) A civil engineer is analyzing the compressive strength of concrete. It is known that the compressive strength has population standard variance o2 = 1000 (psi)?. A random sample of 15 specimens has a mean compressive strength of x = 3250 psi. a. To construct a 90% confidence interval on the population mean of compressive strength of concrete, do you need any further assumptions? If yes, please state your assumption and the theorem you need to construct this confidence interval; if no, please state which theorem you can directly apply and why. b. Based on your conclusion or assumption in part a, construct a 90% two-sided confidence interval on the mean compressive strength of concrete. C. Based on your conclusion or assumption in part a, suppose it is desired to estimate the compressive strength with an error that is less than 12 psi at 99% confidence. What is the minimum required sample size? d. Suppose o2 is unknown, instead, the same random sample has sample variance 1000 (psi). Is the conclusion you made in part (a) still needed to construct the confidence interval? Construct a 90% confidence interval on the mean compressive strength of concrete. e. Compare the results between part (b) and part (d). Show your finding and try to explain the cause(s) of your finding.