# 09_18_09ans - industrial region 4.4 3.7 5.1 4.3 4.7 3.7 3.5...

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STAT 409 Examples for 09/18/2009 Fall 2009 1. A manufacturer of TV sets wants to find the average selling price of a particular model. A random sample of 25 different stores gives the mean selling price as \$342 with a standard deviation of \$14. Assume the prices are normally distributed. Construct a 95% confidence interval for the mean selling price of the TV model. σ is unknown. n = 25 – small. The confidence interval : n s t 2 X α ± . n - 1 = 25 - 1 = 24 degrees of freedom. 95% confidence level, α = 0.05, α / 2 = 0.025, 2 t α ( 24 ) = 2.064 . 25 14 064 . 2 342 ± 342 ± 5.78 ( 336.22 ; 347.78 ) 2. Measurements of the acidity (pH) of rain samples were recorded at 9 sites in an
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Unformatted text preview: industrial region. 4.4 3.7 5.1 4.3 4.7 3.7 3.5 4.6 4.7 Construct a 90% confidence interval for the mean acidity of rain in that region. (Assume the rain acidity follows a normal distribution.) [ Hint: Σ x = 38.7, Σ x 2 = 168.83. ] 9 7 38 i x x . n = = ∑ = 4.3. ( 29 ( 29 8 42 . 2 8 9 7 . 38 83 . 168 1 i i 2 2 2 2 x x s =-=--= ∑ ∑ n n = 0.3025. s = 3025 . = 0.55. σ is unknown. n = 9 – small. The confidence interval : n s t 2 X ⋅ α ± . n-1 = 9 -1 = 8 degrees of freedom. 90% confidence level, α = 0.10, α / 2 = 0.05, 2 t α ( 8 ) = 1.860 . 9 55 860 1 3 4 . . . ± 4.30 ± 0.341 ( 3.959 ; 4.641 )...
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