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COLLEGE OF NATURAL AND MATHEMATICAL SCIENCES DEPARTMENT OF MATHEMATICS AND STATISTICS $T2102: STATISTICAL INFERENCE, TESTI Time Allowed; 60 Minutes Instructions to candidates I. There are TWO questions in this test. Answer BOTH questions. 2. All answers and rough work should be written on the answer booklet provided and NOT con the question paper. 3. All regulations guiding the administration of university examinations apply. QUESTIO’ |. A manufacturer of a certain product claims that 90% of all orders are shipped within 12 hours of being received. Suppose wholesalers placed 121 orders of different sizes and at different times of day; 102 orders were shipped within 12 hours. REQUIRE! fa) Confirm that the sample is large enough to assume that the sample proportion is normally distributed (2 Marks) (b) State the shape, mean, and standard deviation for the sampling distribution of the sampled proportion. (4 Marks) (©) Find the probability that a sample of size 121 would produce a sample proportion so low as observed in this sample. (4 Marks) 2. Consider a normal population with a given mean 4 and unknown variance 0, REQUIRED: (@) Derive the method of moments estimator of 6? (3 Marks) (b) Derive the maximum likelihood estimator of o” (7 Marks) be] CamScanner