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7. (20 points) A construction engineer collected data from some construction sites on the quantity of gravel (in metric tons) used in mixing concrete. The quantity of gravel for n = 24 sites 4861, 5158, 8642, 2896, 7654, 9891, 8381, 6215, 1116, 7918, 2313, 8114, 3517, 8852, 5712, 4312, 8023, 1215, 3598, 2429, 8211, 4613, 9168, 6819, has En = 139628 = 979604548 i= 1 i= 1 Assume that the population is normal. (a) (10 points) What can one assert with 90% confidence about the maximum error if i is used as a point estimate of the true population mean amount of gravel used in concrete mixes? Construct a 90% confidence interval for the true population mean quantity of gravel in concrete mixes. (b) (10 points) Construct a test of hypotheses with the intent of showing that the mean gravel usage in the concrete mix is less than 6000 tons at a = 0.1 significant level. 8. (10 points) A manufacturer claims that the average tar content of a certain kind of cigarette is / = 14.0 mg. In an attempt to show that it differs from this value, five measurements are made of the tar content (mg per cigarette): 14.5, 14.2, 14.4, 14.3, 14.6 Show that the difference between the mean of this sample, i, and the average tar claimed by the manufacturer, / = 14.0 is significant at o = 0.05. Assume normality