prob4sol - The Hong Kong University of Science and...

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The Hong Kong University of Science and Technology ISMT 111 - Business statistic Problem Sheet 4 Solutions 1. A 95% C. I. for μ 1 - 2 is ( x 1 - x 2 ) ± t α /2, n1 + n2 – 2 s p 2 1 1 1 n n + where t 0.025, 12 = 2.179 s p = ) 2 ( ) 1 ( ) 1 ( 2 1 2 2 2 2 1 1 - + - + - n n s n s n = {[(7 - 1)(4) 2 + (7 - 1) (4) 2 ] / (7 + 7 - 2)} ½ = 2 95% C. I. is (7 - 3) ± (2.179)(2)(1/7 + 1/7) ½ = 4 ± 2.3294 = (1.6706, 6.3294) 2. (25.42, 36.58) 3. (69.9141, 93.0859) 4. = (620.13, 8879.87) 5. A 98% C. I. for 1 - 2 is ( x 1 - x 2 ) ± z /2 2 2 2 1 2 1 n s n s + where = 0.02, z 0.01 = 2.326 98% C. I. is (82700 - 78100) ± 2.326 [(7100)2 / 66 + (6300)2 / 57] ½ = 4600 ± 2810.62 = (1789.38, 7410.62)
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6. Let x be the number of consumers out of 200 who identify Pepsi. x ~ Bin (200, ½ ) p ˆ = x / n ~ N ( p , pq / n ) p ˆ ~ N (1 / 2, 1 / 800) (a) P(0.45 < p ˆ < 0.6) = P({(0.45 - 0.5) / (0.00125) 1/2 } < z < { (0.6 - 0.5) / (0.00125) 1/2 }) = P( -1.414 < z < 2.828 ) = 0.4207 + 0.4977 = 0.9184
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This note was uploaded on 02/27/2010 for the course ISOM ISOM111 taught by Professor Anthonychan during the Spring '09 term at HKUST.

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prob4sol - The Hong Kong University of Science and...

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