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A civil engineer is analyzing the compressive strength of concrete. It is known that the compressive strength has population standard variance σ 2
A civil engineer is analyzing the compressive strength of concrete. It is known that the compressive strength has population standard variance σ 2=1000(psi) 2
.A random sample of 15 specimens has a mean compressive strength of X
ˉ
=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 σ 2
is unknown, instead, the same random sample has sample variance 1000 (psi) 2
. 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.
In order to construct a 90%confidence intervalon the population mean of compressive strength of concrete, no further assumptions are needed.Why are no further assumptions needed to construct the confidence interval?No further assumptions are needed because the problem statement already provides thepopulationstandard variance and a random sample of 15 specimens with a mean compressive strength With these given values, we can directly apply the Central Limit Theorem.The Central LimitTheoremstates that for a large enough sample size, the distribution of sample means will be approximately normal, regardless of the shape of the population distribution. In this case, the sample size of 15 may be considered large enough to satisfy the requirements of the Central Limit Theorem.Using the sample mean, the population standard variance, and the critical value associated with a 90% confidence level, a two-sided confidence interval can be constructed using the formula:where Z is the critical valuecorrespondingto the desired confidence level, σ is the population standard deviation, and n is the sample size.Learn more aboutconfidence intervalbrainly.com/question/32546207#SPJ11...