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Dr. Penelope Nicholls is interested in exploring a possible connection between high plasma homocysteine (a toxic amino acid created by the body as it metabolizes protein) levels and cardiac hypertrophy (enlargement of the heart) in humans. Because there are many complex relationships among human characteristics, it will be difficult to answer her research question due to a significant risk that confounding factors will cloud her inferences. She wants to be sure that any differences in cardiac hypertrophy are due to high plasma homocysteine levels and not to other factors. Consequently, she needs to design her experiment carefully so that she controls lurking variables to the extent possible. Therefore, she decides to design a two-sample experiment with independent sampling: one group will be the experimental group, the other a control group. Knowing that many factors can affect the degree of cardiac hypertrophy (the response variable), Dr. Nicholls controls these factors by randomly assigning the experimental units to the experimental or control group. She hopes the randomization will result in both groups having similar characteristics.
In her preliminary literature review, Dr. Nicholls uncovered an article in which the authors hypothesized that there might be a relationship between high plasma homocysteine levels in patients with end-stage renal disease (ESRD) and cardiac hypertrophy. She has asked you, as her assistant, to review this article.
Upon reading the article, you discover that the authors used a nonrandom process to select a control group and an ESRD group. The researchers enlisted 75 stable ESRD patients into their study, all on hemodialysis for between 6 and 312 months. The control group subjects were chosen so as to eliminate any intergroup differences in terms of mean blood pressure (BP) and gender. In an effort to minimize situational contaminants, all physical and biochemical measurements were made after an overnight fast. The results for the control and ESRD groups are reproduced in the tables below.
1. Which type of sampling method, independent or dependent, was used in this experiment? Explain.
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Chapter 11 Solutions
Fundamentals of Statistics Plus MyLab Statistics with Pearson eText - Title-Specific Access Card Package (5th Edition)
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- iid 1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution depend on the mean and variance of the underlying random variables (i.e., the population mean and variance). The approximation can be written to emphasize this, using the expec- tation and variance of one of the random variables in the sample instead of the parameters μ, 02: YNEY, · (1 (EY,, varyi n For the following population distributions f, write the approximate distribution of the sample mean. (a) Exponential with rate ẞ: f(y) = ß exp{−ßy} 1 (b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ } г( (c) Poisson with rate λ: P(Y = y) = exp(-\} > y! y²arrow_forward2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and the standard normal CDF Fz(·).arrow_forwardmatharrow_forward
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