E. Le coefficient de corrélation entre l'âge et le risque d'avoir un cancer est de \( -0,98 \). Cela signifie que : 1. Plus l'âge est élevé, plus les individus ont le cancer 2. Plus les individus sont jeunes, plus le risque de cancer est faible 3. Moins l'âge est élevé, moins le risque de cancer est élevé 4. Plus les individus sont âgés, plus le risque de cancer est faible 5. Aucune de ces propositions n'est correcte F. Pour comparer la façon dont des éléments évoluent dans le temps on utilisera de préférence un graphique : 1. Circulaire aussi appelé Camembert 2. A barres horizontales (3. A barres verticales 4. En nuage de points 5. Aucune de ces propositions n'est correcte G. Soit la répartition des salaires de l'usine EasyJob telle que dans le tableau ci-dessous : \( : 0-e+1 / 2=11 \). \begin{tabular}{|lc|c|c|c|c|} \hline & 11 & 13,5 & 16,75 & 20,25 & 23,5 \\ \hline Salaire horaire en \( € \) & {\( [10 ; 12[ \)} & {\( [12 ; 15[ \)} & {\( [15 ; 18,5[ \)} & {\( [18,5 ; 22[ \)} & {\( [22 ; 25[ \)} \\ \hline Nombre d'employés & 120 & 190 & 240 & 100 & 50 \\ \hline \end{tabular} 1. Quelle est la moyenne? moyenne it mileul 2. Quelle est la médiane? \[ 15,58 \] H. Un recensement des salaires belges des cadres de société suit une loi Normale de moyenne \( 46.500 € \) (brut annuel) et d'écart-type de \( 708 € \) (brut mensuel). A partir de quel salaire brut annuel peut-on considérer le cadre comme riche \( (5 \% \) de la population)? I. Une variable aléatoire \( X \) suit une loi normale de \( \mu=8 \) et \( \sigma=3 \). Quelle valeur faut-il donner à a pour que \( \mathrm{P}(8 \leq \mathrm{X} \leq a)=0,4573 \) ? \( \qquad \) \[ \begin{array}{l} N(\delta, a) \\ \begin{array}{l} \text { LRA }=8 \\ 0=3 \\ P(8 \leq x \mid \leq a)=0,4573 \end{array} \\ \text { p }(8-8 \leq z \leq a)=0,4573: p(0 \leq \sqrt{ }=0,4573 \\ z: \frac{x-\mu}{e} \quad \Rightarrow 1,72=\frac{x-8}{\Rightarrow 1,72,3^{3}+8=} \\ \end{array} \]
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Fall 2018 Version 2 1) Draw a Box Plot for the data { 1, 1, 2, 3, 4, 6, 7, 8, 9, 10, 4, 6, 8, 9, 2, 4, 8, 10, 12, 13, 14} 2) A group of 51 randomly selected students have a mean score of 25.4 with a standard deviation of 3.1 on a placement test. What is the 90 percent confidence interval for the mean score, μ, of all students taking the test? A) 24.5 < μ < 26.3 B) 24.3 < μ < 26.5 C) 24.4 < μ < 26.4 D) 24.7 < μ < 26.1 Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. 3) x | 0 3 4 5 12 y | 8 2 6 9 12 A) ŷ = 4.88 + 0.525x B) ŷ = 4.98 + 0.725x C) ŷ = 4.98 + 0.425x D) ŷ = 4.88 + 0.625x 4) Let Z be standard normal, Find P(Z < 0.97) A) 0.8315 B) 0.8078 C) 0.8340 D) 0.1660 5) Various temperature measurements are recorded at different times for a particular city. The mean of 20°C is obtained for 40 temperatures on 40 different days. Assuming that σ = 1.5°C, test the claim that the population mean is 23°C. Use a 0.05 significance level. 6) A spinner has equal regions numbered 1 through 21. What is the probability that the spinner will stop on an even number or a multiple of 3? A) 2/3 B) 17 C) 1/3 D) 10/9 7) The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month? A) 40.82% B) 9.18% C) 35.31% D) 90.82% 8) The table below shows the soft drinks preferences of people in three age groups. cola | root beer | lemon-lime under 21 years of age | 40 | 25 | 20 between 21 and 40 | 35 | 20 | 30 over 40 years of age | 20 | 30 | 35 One of the 255 subjects is randomly selected, find the probability that the person drinks root beer given that they are over 40. A) 6/17 B) 2/5 C) 2/7 D) None of the above is correct.
Madhur L.
The following questions are related to a generalized linear regression model. What are the 3 components of a generalized linear model? For a logistic regression of lung cancer incidences (1=developed lung cancer, 0=did not develop lung cancer) with smoking statuses (1=current or past smoker, 0=never smoker), specify the 3 components that you identified in part a. A study was conducted to investigate the effects of AZT treatment on the development of AIDS symptoms among HIV-infected veterans. Among 170 individuals who took AZT, 25 developed the symptoms of AIDS by the end of the study. Among the other 168 individuals who did not take AZT (placebo group), 44 developed the symptoms of AIDS. Construct a two-by-two table. Use AIDS symptoms as columns and AZT treatment as rows. Based on the table constructed in a., calculate the odds of AIDS in the treatment group, odds of AIDS in the placebo group, and the odds ratio of AIDS comparing the treatment and placebo group. If we fit a logistic regression model of the development of AIDS symptoms on AZT based on the data provided, write down the model (No need to specify three components in GLM, write one formula connecting the probability of developing AIDS and AZT. Hint: you need to create a dummy variable for AZT). Without fitting the regression model in c. via Stata, give estimates of the coefficient betas. Suppose race (1=white, 0=nonwhite) is a potential confounder and we fit a logistic regression model for the development of AIDS symptoms on AZT (1=users, 0=nonuser), race (1=white, 0=nonwhite), and the interaction between AZT and race. Using the output shown below, estimate the probability of developing AIDS symptoms during the study follow-up for a nonwhite AZT user. [Stata] Property Valuation: Scientific mass appraisal uses linear regression methods to assess property valuation. Twenty-four observations were obtained from a property listing for Champaign IL. The problem is to find the best fitting regression model to predict the sales price (y) using the following independent variables: taxes in $1000s of dollars (x1), number of bedrooms (x2), age of the home in years (x3). The data set is stored in the midterm.dta file. Answer the following questions, justifying with appropriate analyses. Do not just answer yes or no, you must justify your response and provide data to back it up. In a fitted regression model that relates the sale price to taxes and building characteristics, would you include all the variables? (Hint: Are all the variables significant?) A veteran real estate agent has suggested that a model with taxes and the number of bedrooms should adequately describe the sales price. Do you agree? Present what you consider to be the most adequate model or models for predicting the sale price of homes in Champaign IL. ID x1 x2 x3 y 1 4.918 4 42 25.9 2 5.021 4 62 29.5 3 4.543 3 40 27.9 4 4.557 3 54 25.9 5 5.06 3 42 29.9 6 3.891 3 56 29.9 7 5.898 3 51 30.9 8 5.604 3 32 28.9 9 5.828 3 32 35.9 10 5.3 3 30 31.5 11 6.271 2 30 31 12 5.959 3 32 30.9 13 5.05 2 46 30 14 8.246 4 50 36.9 15 6.697 3 22 41.9 16 7.784 3 17 40.5 17 9.038 3 23 43.9 18 5.989 3 40 37.9 19 7.542 3 22 37.9 20 8.795 4 50 44.5 21 6.083 3 44 37.9 22 8.361 4 48 38.9 23 8.14 3 3 36.9 24 9.142 4 31 45.8
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22) Read the following and answer questions 22-26 In the 1980's it was believed that congenital abnormalities affected about 5% of the nation's children. Somepeople believe that an increase in the chemicals in the environment has led to an increase in the number of abnormalities. A recent study examined 384 randomly selected children and found that 23 of them showed signs of an abnormality. Does this provide evidence that the risk of congenital abnormalities has increase? Use ̑ = 0.05 to make your decision. What would the appropriate hypotheses be for this problem? A) H0 : p = 0.05; Ha : p > 0.05 B) H0 : p = 0.05; Ha : p not equal 0.05 C) H0 : p < 36; Ha : p > 36 D) H0 : p = 0.05; Ha : p < 0.05 23) What would the standard error be for this problem? A) 0.011122 B) 0.0133 C) 0.7911 D) 10^(-4) 24) What is the resulting test statistic? A) 0.89 B) 0.623 C) 0.712 D) -0.89 25) What is the resulting p-value? A) 0.1867 B) 0.224 C) 0.712 D) 0.1494 26) What is the appropriate conclusion? A) The p-value is greater than alpha. We DO NOT reject the null hypothesis. This DOES NOT provide evidence that the risk of congenital abnormalities has increased. B) The p-value is greater than alpha. We DO NOT reject the null hypothesis. This provides evidence that the risk of congenital abnormalities has increased. C) The p-value is smaller than alpha. We reject the null hypothesis. This DOES NOT provide evidence that the risk of congenital abnormalities has increased. D) The p-value is greater than alpha. We reject the null hypothesis. This provides evidence that the risk of congenital abnormalities has increased.
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