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hw6sol - 2 1 p p we can ’ t say that the premiere of ‘...

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Business Statistics Lecture Sections (Prof. Inchi HU) Assignment 6 Solution (Problem Sheet 4 #5, 9, 13) 5. Let 1 m , 2 m be the mean value of loans processed during April and May respectively. A 98% Confidence Interval for 1 2 m m - is ( 29 ( 29 57 6300 66 7100 33 . 2 78100 82700 2 2 1 2 1 2 2 2 01 . 0 1 2 + ± - = + ± - n s n s z X X ( 29 4497 . 7415 , 5503 . 1784 4497 . 2815 4600 = ± = 9. (a) 6121 . 0 165 101 ˆ 1 = = p A 95% confidence interval for p 1 is ( 29 ( 29 .6865 0 , 5378 . 0 0743 . 0 6121 . 0 165 6121 . 0 1 6121 . 0 96 . 1 6121 . 0 ˆ ˆ ˆ 1 1 1 025 . 0 1 = ± = - ± = ± n q p z p (b) In repeated sampling, 95% of the confidence intervals constructed in this way will cover the true proportion p 1 . (c) 05 . 0 = e and 6121 . 0 ˆ 1 = p 16 . 384 05 . 0 5 . 0 5 . 0 96 . 1 ˆ ˆ 2 2 2 1 1 2 025 . 0 1 = × × = e q p z n 385 Take 1 = n . (d) The point estimate of 2 1 p p - is 0732 . 0 180 97 165 101 ˆ ˆ 2 1 = - = - p p . A 95% confidence interval for 2 1 p p - is ( 29 ( 29 ( 29 165 4611 . 0 5389 . 0 165 3879 . 0 6121 . 0 96 . 1 0732 . 0 ˆ ˆ ˆ ˆ ˆ ˆ 2 2 2 1 1 1 025 . 0 2 1 + ± = + ± - n q p n q p z p p ( 29 0.1773 , 0308 . 0 1041 . 0 0732 . 0 - = ± (e) Since zero lies within the 95% confidence interval for
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Unformatted text preview: 2 1 p p-, we can ’ t say that the premiere of ‘ The Cosby Show ’ is more popular than premiere of ‘ The X-files ’ . 13. (a) Let µ be the mean waiting time of the bank ’ s customers. A point estimate for µ is 79 . 5 = X . A 95% confidence interval for µ is ( 29 5828 . 6 , 9972 . 4 7928 . 79 . 5 50 86 . 2 96 . 1 79 . 5 025 . = ± = × ± = ± n s z X (b) We have 95% confidence to say that the interval can enclose m . (c) ( 29 872 Take 2470 . 871 2 5 . 86 . 2 58 . 2 2 2 2 2 2 2 005 . = ⇒ = = n e s z n Hence, 822 (= 872 - 50) additional customer have to be selected....
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