Homework 4 solutions

Homework 4 solutions - Statistics 5021 Homework 4...

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Unformatted text preview: Statistics 5021 Homework 4 (solutions) There are 20 total points (1 point for each part of each question and 8 points for handing in the assignment). One question will be graded for correctness. This homework is due Thursday, March 3 in your lab section. 1. The data are 35 measured systolic blood pressures in mmHg 159 92 102 92 90 91 96 91 118 136 91 90 111 92 90 91 90 151 92 90 146 94 90 90 91 90 176 95 90 90 159 92 109 90 106 The observed sample mean is x = 104 . 6571 mmHg and the observed sample standard deviation is s = 24 . 53082 mmHg. A researcher feels that using the Normal distribution to model systolic blood pressures for the population is problematic. (a) Compute a 95% confidence interval for , the population distribution mean sys- tolic blood pressure. State all assumptions made and interpret the interval. Solution: We must assume that the systolic blood pressure measurements x 1 ,...,x 35 are a realization of a random sample from a distribution with mean and standard deviation , and that n = 35 is sufficiently large to account for our not using the Normal distribution to model systolic blood pressures for the population. A confidence level of 95% corresponds to = 1- . 95 = 0 . 05, thus t 1- / 2 ,n- 1 = t . 975 , 34 = qt (0 . 975 , 34) = 2 . 032245. Plugging in the known quantities to the formula, x t 1- / 2 ,n- 1 s n = 104 . 6571 2 . 032245 24 . 53082 35 = (96 . 231 , 113 . 084) Our interpretation is that we are approximately 95% confident that , the pop- ulation distribution mean systolic blood pressure, is between 96.231 mmHg and 113.084 mmHg. (b) Suppose that the 3rd and 4th measurements are two systolic blood pressures measured on the same individual. Given this information, explain why it is un- reasonable to assume that x 1 ,...,x 35 are a realization of a random sample from a distribution. Solution: The 3rd and 4th measurements: x 3 ,x 4 are a realization of X 3 ,X 4 which are almost certainly dependent random variables, since these are repeated measurements on the same individual and are certainly associated. (e.g. knowl- edge that the first measurement on this subject was under 110 mmHg will impact the uncertainty about the second, yet-to-be measured systolic blood pressure for this individual). This would imply that x 1 ,...,x 35 are not a realization of a random sample, since...
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This note was uploaded on 05/06/2011 for the course STAT 5021 taught by Professor Staff during the Spring '08 term at Minnesota.

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Homework 4 solutions - Statistics 5021 Homework 4...

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