4. {5 points] A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with (11'2 =1000 psi: .A random sample of 12 specimens has a mean compressive strength of E =3250 psi. Construct a 95% twosided confidence interval on mean compressive strength. Comment on whether a 99% twosided confidence interval would be wider or narrower than the one you found. 5. An article in the Journal ofC'omposite Materials [December 1989, Vol. 23(12}, pp. 12001215] describes the effect of delamination on the natural frequency of beams made from composite laminates. Five such delaminated beams were subjected to loads, and the resulting frequencies {in hertz} were as follows: 230.55, 233.05, 232.53, 223.43, 232.53, 230.55, 233.05, 232.53, 223.43, 232.53 a. {5 points] Check the assumption of normality in the population. Show work to support your conclusion. b. (5 points) Calculate a 90% two-sided confidence interval on mean natural frequency.6. An article in The Engineer ("Redesign for Suspect Wiring," June 1990] reported the results of an investigation into wiring errors on commercial transport aircraft that may display faulty information to the ight crew. Such a wiring error may have been responsible for the crash of a British Midland Airways aircraft in January 1989 by causing the pilot to shut down the wrong engine. Of 1600 randomly selected aircraft, 8 were found to have wiring errors that could display incorrect information to the flight crew. a. (5 points) Find a 95% confidence interval on the proportion of aircraft that have such wiring errors. b. [5 points] Suppose that you use the information in this example to provide a preliminary estimate of ,0. How large a sample would be required to produce an estimate ofp that we are 95% condent differs from the true 1uralue by at most 0.003