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

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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 - 0 . 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 0 . 355(1 - 0 . 355) 107 = 0 . 046 . The 95% Agresti-Coull confidence interval is ˜ p ± 1 . 96 SE ˜ p = 0 . 355 ± 1 . 96(0 . 046) = (0 . 265 , 0 . 445) . We are 95% confident that the true proportion p of obese individuals from this population is between 0 . 265 and 0 . 445 (or equivalently, between 26.5% and 44.5%).
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