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old midterm solution - The University of Western Ontario...

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1 The University of Western Ontario Biology/Stats 2244 Old midterm questions NOTE: These questions were taken from an exam offered in a previous term when a different textbook was used. In the term that this exam was offered the following topics were not included: counting rules (Ch 3.8) and the binomial distribution and CI’s for p (Chs. 4-3, 4-4, 5-6 & 6-2) . Therefore, questions on these topics are not included in this sample exam but will appear on your midterm. Also, we used the letters Y and y as the random variable of interest throughout this exam. So, please treat Y and y as X and x, respectively to match the notation we’ve been using use this term. 1. In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200 adults are randomly selected for a market research campaign. Which of the following accurately describes the distribution of IQ in this population? A. exactly normal B. approximately N(112,20) C. approximately N(112,1.4) D. not enough information to determine All we are told about the population is that it has mean 112 and standard deviation 20. We don’t know if it is normal, approximately normal or neither. (Answer = D) 2. Refer to the previous question. What is the probability that the mean IQ of 200 randomly selected adults will be greater than 110? Regardless of the normality of the population, n=200 here so the Central Limit Theorem (CLT) applies. We are asked for ( ) . 110 > Y P Due to the CLT the sampling distribution of Y is approximately . 200 20 , 112 N So, in terms of the Z distribution, ( ) ( ) . 41 . 1 200 20 112 110 110 - > = - > = > Z P Z P Y P Table 3 gives us ( ) ( ) . 9207 . 0 0793 . 0 1 41 . 1 1 41 . 1 = - = - - = - > Z P Z P (Answer = C) 3. What is the definition of a random variable?
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Choice by choice: 4. A group of 10 patients with end-stage renal disease were given the drug epoetin. The average hemoglobin level of the patients was 10.3 g/dLi and the SD was 0.9 g/dLi. Construct a 99.9% confidence interval for the true mean hemoglobin level for the population of all patients with end-stage renal disease. The CI is 10.3 ± ______. A. 0.94 B. 1.31 C. 1.36 D. Not enough information to construct a valid interval. We are given s and we do not have σ so it looks like a t CI would be appropriate for this question. However, we know nothing about the distribution of the population (hemoglobin level of end-stage renal disease patients) and n is only 10 so we cannot use the Central Limit Theorem. We would need to know if the distribution was at least roughly symmetric to use the t distribution.
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