**Unformatted text preview: **CHM 241 Exam 1 Name___________________________________ (Print) CALCULATIONS. Show your calculation to get full credits. Just answer 10 questions from the test. 1. For the numbers 116.0, 97.9, 114.2, 106.8, and 108.3, use your calculator to find the mean (2 points), standard deviation (2 points), range (2 points), and 95% interval for the mean (2 points). Using the Q test, decide whether the number 97.9 should be discarded (2 points). 2. Suppose that the mileage at which 10,000 sets of automobile brakes had been 80% worn through was recorded. The average was 62,700 miles, and the standard deviation was 10,400 miles. (a) What fraction of brakes is expected to 80% worn in less than 40,860 miles? (5 points) (b) What fraction is expected to 80% worn at a mileage between 57,500 and 71,020 miles? (5 points) 3. A manufacturer tested the lifetime of 4768 electric light bulbs, and found the mean lifetime of the light bulbs were 845.2 hours, with a standard deviation 94.2 hours. Suppose the manufacturer offers to replace free of charge any bulb that burns out in less than 600 hrs. If she plans to sell a million bulbs, how many extra bulbs should be kept available as replacements? (10 points) 1 4. The carbohydrate content of a glycoprotein (a protein with sugars attached to it) is determined to be 12.6, 11.9, 13.0, 12.7, and 12.5 g of carbohydrate per 100 g of protein in replicate analyses. Find the 95% and 99% confidence intervals for the carbohydrate content. (10 points) 5. A reliable assay shows that the ATP (adenosine triphosphate) content of a certain cell type is 111 mol/100 mL. You developed a new assay, which gave the following values for replicate analyses: 117, 119, 111, 115, 120 mol/100 mL (average = 116.4). Can you be 95% confident that your result differs from the "known" value? (10 points) 6. The percentage of an additive in gasoline was measured six times with the following results: 0.13, 0.12, 0.16, 0.17, 0.20, 0.11%. Find the 90% and 99% confidence intervals for the percentage of the additive. (10 points) 7. A trainee in a medical lab will be released to work on her own when her results agree with those of an experienced worker at the 95% confidence level. Results for a blood urea nitrogen analysis are shown below. (10 points) Trainee: mean = 14.57 mg/dL s = 0.53 mg/dL n = 6 samples Experienced worker: mean = 13.95 mg/dL s = 0.42 mg/dL n = 5 samples (a) What does the abbreviation dL stand for? (b) Should the trainee be released to work alone? 2 8. The Ti content (wt%) of five different ore samples (each with a different Ti content) was measured by each of two methods. Do the two analytical techniques give results that are significantly different at the 95% confidence level? (10 points) 9. Hydrocarbons in the cab of an automobile were measured during trips on the New Jersey Turnpike and trips through the Lincoln Tunnel connecting New York and New Jersey.14 The total concentrations (standard deviations) of m and p xylene were Turnpike: 31.4 30.0 g/m3 (32 measurements) Tunnel: 52.9 29.8 g/m3 (32 measurements) Do these results differ at the 95% confidence level? At the 99% confidence level? (10 points) 10. A Standard Reference Material is certified to contain 94.6 ppm of an organic contaminant in soil. Your analysis gives values of 98.6, 98.4, 97.2, 94.6, and 96.2 ppm. Do your results differ from the expected result at the 95% confidence level? If you made one more measurement and found 94.5, would your conclusion change? (10 points) 3 11. Using the Q test, decide whether the value 216 should be rejected from the set of results 192, 216, 202, 195, and 204. (10 points) 12. Nitrite NO2 was measured by two methods in rainwater and unchlorinated drinking water. The results standard deviation (number of samples) are given in the following table. (10 points) (a) Do the two methods agree with each other at the 95% confidence level for both rainwater and drinking water? (b) For each method, does the drinking water contain significantly more nitrite than the rainwater (at the 95% confidence level)? 4 Equations: t calculated = d sd n Qcalculated = Gap Range 5 Tables: 6 7 ...

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