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05exS_p1

# 05exS_p1 - √ n 1 176> z ∗ 3 √ 70 z 6 1 176 ∗ √...

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ISOM111 Business Statistics (Fall 2010) Solutions for Tutorial Exercise 5 1. Let X be the number of recovery days by new therapy and μ be its mean. (a) x = 12 σ = 3 n = 70 As n = 70 > 30 , by CLT, X N ( μ, σ 2 70 ) The 95% con fi dence interval for the mean recovery days by new therapy is : x ± z 0 . 025 ( σ n ) = 12 ± 1 . 96( 3 70 ) = (11 . 2972 , 12 . 7028) (b) x = 12 σ = 3 n = 25 As we don’t know the distribution of X & n = 25 < 30 assume X N X N ( μ, σ 2 70 ) The 95% con fi dence interval for the mean recovery days by new therapy is : x ± z 0 . 025 ( σ n ) = 12 ± 1 . 96( 3 25 ) = (10 . 824 , 13 . 176) (c) B = 0 . 5 B > n n > ( 2 . 576 3 0 . 5 ) 2 > 238 . 8879 Take z = 2 . 576 , n > 238 . 8879 n = 239 Take z = 2 . 575 , n > 238 . 7025 n = 239 Take z = 2 . 58 , n > 239 . 6304 n = 240 (d) From part (b), B = 1 . 176 B >
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Unformatted text preview: √ n 1 . 176 > z ∗ 3 √ 70 z 6 1 . 176 ∗ √ 70 3 6 3 . 28 With z = 3 . 28 , con f dence level = (0 . 49948 ∗ 2) ∗ 100% = 99 . 89% (e) 92% C.I. for the di f erence in mean recovery time is : Take z = 1 . 75 ¡ X 1 − X 2 ¢ ± Z . 04 ∗ r σ 2 1 n 1 + s 2 2 n 2 = (12 − 14) ± 1 . 75 ∗ r 3 2 70 + 2 2 60 = ( − 2 . 773251 , − 1 . 226749) Take z = 1 . 76 ¡ X 1 − X 2 ¢ ± Z . 04 ∗ r σ 2 1 n 1 + s 2 2 n 2 = (12 − 14) ± 1 . 76 ∗ r 3 2 70 + 2 2 60 = ( − 2 . 777669 , −− 1 . 222331) 1...
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