2005 Final

# 2005 Final - MATH 203 Final Examination December 6 2005...

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MATH 203 Final Examination December 6, 2005 Student Name: Student Number: Faculty of Science FINAL EXAMINATION MATHematics 203 Principles of Statistics I Tuesday, December 6th 9 a.m. - 12 Noon Answer directly on the test (use front and back if necessary). Calculators are allowed. One 8.5” × 11” two-sided sheet of notes is allowed. Language dictionaries are allowed. There are 16 pages to this exam and 3 pages of tables. The total number of marks for the exam is 100. Examiner: Professor Russell Steele Associate Examiner: Professor Masoud Asgharian 1

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MATH 203 Final Examination December 6, 2005 Question 1: (8 points) The amount of lead in a certain type of soil, when released by a standard extraction method, averages 86 parts per million (ppm). A new extraction method is tried on 40 specimens of the soil, yielding a mean of 83 ppm lead and a standard deviation of 10 ppm. Test the hypothesis that the new method yields less lead than the old method (choose any reasonable signiFcance level). (8 points) 2
MATH 203 Final Examination December 6, 2005 Question 2: (6 points) Assume that Y is normally distributed with mean 0.05 and variance 0.25. Calculate the follow- ing probabilities: (a) Pr ( Y > - 0 . 05) = (2 points) (b) Pr ( - 0 . 40 < Y < 0 . 50) = (2 points) (c) Pr ( Y = 0 . 05) = (2 points) 3

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MATH 203 Final Examination December 6, 2005 Question 3: (16 points) A Master’s student in Environmental Engineering was studying the efect oF two types oF treat- ment on bacterial growth in drinking water. The two treatments were UV40 (ultraviolet light) and PAA+UV20 (phenylacetic acid and ultravoiolet light). Each day the student sampled water From the same source, poured it into two containers and then randomly assigned a treatment to each container. The log bacterial growth was then measured aFter three hours oF being exposed to a light source For each container. The student did this on 33 separate days. Assume the days were Far enough apart so that the samples were independent and diferent For diferent days. The goal oF the analysis is to see iF there is a diference between treatments with respect to suppressing bacterial growth. UV40 PAA2+UV20 -1.0 -0.5 0.0 0.5 1.0 1.5 Log Growth by Treatment Difference btw Trts by Day UV40 PAA+UV20 Dif by day (UV40 - PAAUV20) Min -0.7 -0.9 0.10 25%ile 0.8 -0.2 0.8 50%ile 1.1 0.2 1.0 75%ile 1.4 0.3 1.4 Max 1.8 0.9 1.9 Mean 1.06 0.04 1.02 StDev 0.51 0.43 0.46 4
MATH 203 Final Examination December 6, 2005 (a) Test the hypothesis that there is no mean bacterial growth after 3 hours for each treatment

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2005 Final - MATH 203 Final Examination December 6 2005...

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