1. A random sample has been taken from a normal distribution. Output from a software package follows: Variable N Mean SE Mean StDev Variance Sum x 10 0.53 1.7 251.848 a. Fill in the missing quantities. b. Find a 95% CI on the population mean. 2. An article in Nuclear Engineering International (February 1988, p. 33) describes several characteristics of fuel rods used in a reactor owned by an electric utility in Norway. Measurements on the percentage of enrichment of 12 rods were reported as follows: 8.24 8.25 8.20 8.21 8.26 8.26 8.23 8.23 8.19 8.23 8.24 8.20 8.25 8.28 8.24 (a) Check the assumption of normality for rod diameter with a histogram. (b) Calculate a 95% two-sided confidence interval on mean rod diameter. (c) Calculate a 95% upper confidence bound on the mean. Compare this bound with the upper bound of the two-sided confidence interval and discuss why they are different 3. The compressive strength of concrete is being tested by a civil engineer who tests 12 specimens and obtains the following data: 2216 2237 2225 2301 2318 2255 2249 2204 2281 2263 2275 2295 (a) Check the assumption that compressive strength is normally distributed. Include a graphical display in your answer. (b) Construct a 95% two-sided confidence interval on the mean strength. (c) Construct a 95% lower confidence bound on the mean strength. Compare this bound with the lower bound of the two-sided confidence interval and discuss why they are different. 4. A particular brand of diet margarine was analyzed to determine the level of polyunsaturated fatty acid (in percentages). A sample of six packages resulted in the following data: 16.8, 17.2, 17.5, 16.9, 16.5, 17.0. Assume the level of polyunsaturated fatty acid is normal distributed. b. Calculate a 99% confidence interval on the mean p. Provide a practical interpretation of this interval. c. Calculate a 99% lower confidence bound on the mean. Compare this bound with the lower bound of the two-sided confidence interval and discuss why they are different. 5. A rivet is to be inserted into a hole. A random sample of n = 17 parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measurements is s=0.008 mm. Construct a 99% lower confidence bound for o². 6. The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.28. Construct a 95% two-sided confidence interval for o². 7. An article in the Australian Journal of Agricultural Research ("Non-Starch Polysaccharides and Broiler Performance on Diets Containing Soyabean Meal as the Sole Protein Concentrate" (1993, Vol. 44(8), pp. 1483-1499)] determined that the essential amino acid (Lysine) composition level of soybean meals is as shown