Final Exam Problems - Elementary Statistics and Probability | STAT 100, Exams of Probability and Statistics

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B. Kedem Summer 2003, STAT 100, Sec. 0101, July 11, 2003 STAT 100 Final Exam 1 (20 pts.) A basket contains 10 potatoes, 3 are good and 7 are bad. Let X be the number of good potatoes in a random sample of size 2 taken from the basket without replacement. a (5). Explain why X does not have a binomial distribution. b (15). Find the expected value of X, 2. (30 pts.) A physical model suggests that the mean temperature increase in the water used as a coolant in a compressor chamber should not be more than 6°C. Temperature increases in the coolant measured on 8 indepen- dent runs of the compressing unit revealed the following data: 6.1, 4.8, 5.4, 4.5, 6.5, 5.9, 6.7, 4.7. a (10). Determine if the data contradict the assertion of the physical model at the 5% significance level. What are your assumptions? b (10), What is the p-value? c (10). Determine a 98% confidence interval for the mean increase of the temperature in the coolant. 3. (15 pts.) Two types of pumpkin fertilizer Fl, F2, are tested on four soil types, A,B,C,D. The weight in pound of the pumpkins after 8 weeks of growth are recorded below. Soil Type A B C D Fl 4 0 7 8 F2 3°05 7 Is there evidence F1 is better (in terms of weight) than F2 ? Suggest a way to test this question, and then execute your test at level 0.05.