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Stat 305 (Ghosh): HW9 Solutions P3246 2 3 (a) You can use equation (6+9), since this is a large sample. The appropriate z for 90% confidence is 1.645. The interval is 98.2 142.7 + 1.645 | = = 142.7431.68 (a) i) (111.02, 174.38]. Now z = 1.96, and the interval is 98.2 142.741.96[——} = 142.74 37.75 = [104.95, 180.45]. This interval is wider than the one from (a). In order te have more confidence of containing the mean, the interval must be wider. To make a 90% one-sided confidence interval, construct a 80% two-sided confidence interval, and use the upper endpoint. The appropriate z for a 80% two-sided confidence interval is 1.28, so the 90% one-sided confidence interval is 98.2 142.7 + 1.28 (33) = 142.7 + 24.65 V26. = 167.35. This value is smaller than the upper endpoint from part (a). Setting the lower endpoint equal to —co requires you to move the upper endpoint in so that the confidence remains at 90%. To make a 95% one-sided confidence interval, construct a 90% two-sided confidence interval, and use the upper endpoint. This was done in part (a), so the 90% one-sided confidence interval is 174.38. This is larger than the answer to (c); in order to achieve higher confidence, you must make the interval “wider”. (e) (111.02, 174.3Gppm is a act of plausible values for the mean aluminum content of samples of recycled PET plastic from the recycling pilot plant at Rutgers University. The method used to construct this interval correctly contains means in 90% of repeated applications. This particular interval either contains the mean or it doesn’t (there is no probability involved). However, because the method is correct 90% of the time, we might say that we have 90% confidence that it was correct this time. 
