Exam2_key - NAME: Stat 205 Exam II Write clearly and show...

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Unformatted text preview: NAME: Stat 205 Exam II Write clearly and show steps for partial credit. This exam is open book. There are four problems. 1. (10 points) The systolic blood pressure Y of a random American adult follows a normal distribution with mean μ Y = 127 mmHg and standard deviation σ Y = 15 mmHg. Let ¯ Y be the sample mean of n = 16 randomly selected individuals. What is Pr ( ¯ Y > 140) ? Answer: Pr ( ¯ Y > 140) = Pr ¯ Y- 127 15 / √ 16 > 140- 127 15 / √ 16 ¶ = P ( Z > 3 . 466) = 1- P ( Z ≤ 3 . 466) = 1- . 9997 = 0 . 0003 . 2. (25 points) A random sample of n = 103 individuals over 20 years old was taken and y = 36 were medically obese. Compute and interpret a 95% Agresti-Coull confidence interval for the proportion p of obese individuals. Answer: ˜ p = y + 2 n + 4 = 38 107 = 0 . 355 . SE ˜ p = r ˜ p (1- ˜ p ) n + 4 = r . 355(1- . 355) 107 = 0 . 046 . The 95% Agresti-Coull confidence interval is ˜ p ± 1 . 96 SE ˜ p = 0 . 355 ± 1 . 96(0 . 046) = (0 . 265 , . 445) ....
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This note was uploaded on 12/14/2011 for the course STAT 205 taught by Professor Hendrix during the Fall '09 term at South Carolina.

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Exam2_key - NAME: Stat 205 Exam II Write clearly and show...

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