1. An article in Technometrics ["Validation of Regression Models: Methods and Examples" (1977, Vol. 19(4), p. 425)] presented the following data (which have been rounded to the nearest whole value) on the motor fuel octane ratings of several blends of gasoline 89 99 90 92 93 88 88 91 95 88 90 83 88 93 88 90 84 90 92 91 93 M 94 88 92 90 91 91 88 94 97 89 90 89 91 89 89 90 84 92 92 90 92 88 93 91 93 89 92 88 94 87 87 89 90 90 91 85 91 94 89 93 90 87 90 91 91 93 93 92 93 89 100 90 89 87 90 96 91 88 92 a. (5 points) Construct a frequency distribution for these data by filling in the table below. Use 8 bins. Lower limit Upper limit Midpoint Frequency Relative frequencyb. (5 points) Use the frequency distribution on the previous page to construct a histogram for these data. 2. An article in Transactions of the Institution of Chemical Engineers (1956, Vol. 34, pp. 280-293) reported data from an experiment investigating the effect of several process variables on the vapor phase oxidation of naphthalene. A sample of the percentage mole conversion of naphthalene to maleic anhydride follows: 4.2, 4.7, 4.7, 5.0, 3.8, 3.6, 3.0, 5.1, 3.1, 3.8, 4.8, 4.0, 5.2, 4.3, 2.8, 2.0, 2.8, 3.3, 4.8, 5.0. a. (5 points) Calculate the sample mean, sample variance, and sample standard deviation. Feel free to use your calculator. b. (5 points) Construct a box plot of the data, and mark the location of outliers (if any) with an asterisk.3. {5 points] Using your calculator, construct a normal probability plot for the octane data from problem 1, and make a sketch of that plot below. From the plot you sketched, does it seem reasonable to assume that octane rating is normally distributed? 4. {5 points] A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with 0'2 = 1000 psi2 . A random sample of 12 specimens has a mean compressive strength of E: 3250 psi. Construct a 95% two-sided condence interval on mean compressive strength. Comment on whether a 99% two-sided confidence interval would be wider or narrower than the one you found. 5. An article in the Journal of Composite 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: 230.66, 233.05, 232.53, 229.43, 232.53, 230.66, 233.05, 232.53, 229.43, 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 flight 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 p. How large a sample would be required to produce an estimate of p that we are 95% confident differs from the true value by at most 0.008