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Final_Exam_Practice_Problem_Solutions

# Final_Exam_Practice_Problem_Solutions - STA 100 Final Exam...

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STA 100: Final Exam Practice Questions For all questions you must show your working. This enables us to understand your thought process, give partial credit and prevent crude cheating. Notes About These Practice Questions: These practice questions are not a practice exam! i.e., you would not be expected to complete all of these questions in the the time given for the exam. Solutions to these questions will be posted after you have had sufficient time to practice them.

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1. HDL Cholestrol, otherwise known as ‘Good’ Cholestrol, has received much attention in re- cent years. Higher levels of HDL are thought to help reduce the risk of heart disease. HDL Cholestrol levels are measured in miligrams per deciliter of blood (mg/dl). You are asked to investigate a possible link between blood pressure and HDL levels. Blood pressure consists of two measurements: systolic and diastolic (both measured in mmHg). For the first part of this question we consider blood pressure as a categorical variable ( bp in the data below) taking three possible values: Low, Medium or High. Example data for six individuals is shown below: id HDL bp 79 38.84 High 142 35.83 Med 147 59.57 Med 148 40.49 Med 153 72.24 Low 163 61.68 Low The mean HDL level for for individuals with high/med/low blood pressure are denoted by μ h , μ m and μ l respectively. (a) Your first question of interest is: ‘Do mean HDL levels vary across blood pressure groups?’ Write down the null hypothesis that you would use to answer this question. H 0 : μ l = μ m = μ h (b) For answering the question posed in Q 1a, write down the response variable. The response variable is HDL level. (c) For answering the question posed in Q 1a, write down the explanatory variable. The explanatory variable is blood pressure level. (d) What statistical method could be used to answer the question posed in Q 1a? Hint: Recall the table given in lecture. We could use Analysis of Variance (ANOVA) to answer the question.
(e) Your boss drops off a bunch of paperwork on your desk. Among the coffee stained papers you notice the following R output: > A1 <- aov(HDL~bp,data=df) > print(summary(A1)) Df Sum Sq Mean Sq F value Pr(>F) bp 2 417.6 208.800 3.0357 0.0508 . Residuals 161 11073.7 68.781 --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 Using this output, conduct a hypothesis test (at level α = 0 . 05) to answer the question posed in Q 1a. You must write down all of the following pieces of information: (1) H 0 (the null hypothesis), (2) H 1 (the alternative hypothesis), (3) The test statistic, (4) The reference distribution (i.e., the distribution of your test statistic under H 0 ), (5) The p - value for your test, (6) Your decision (reject H 0 or do not reject H 0 ), (7) Your conclusion (what this means in terms of blood pressure and HDL). H 0 : μ l = μ m = μ h H 1 : At least one μ i 6 = μ j for i, j ∈ { l, m, h } . The test statistic is: F = Mean Square Between Groups Mean Square Within Groups = 208 . 8 68 . 781 = 3 . 0357 The reference distribution is F 2 , 161 The p - value is p = P ( F 2 , 161 > F ) = P ( F 2 , 161 > 3 . 0357) = 0 . 0508 .

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