A 99% confidence interval (in inches) for the mean height of a population is 66.2 < μ < 67.6. This result is based on a sample of size 144. Construct the 95% confidence interval. (Hint: you will first need to find the sample mean and sample standard deviation).  

Directed Acyclic Graphs (DAGs) (10 points) To complete this section, please review the articles on DAGs in the Week 5 Learning Resources. You may use any drawing tools available to you to create the DAGs requested below, although it does not need to be sophisticated software; for example, Microsoft Word’s Insert Shapes and Text Box features are sufficient tools to create these diagrams. For each of the following epidemiological scenarios, draw a DAG that represents the relationships between the variables: (5 points each) A researcher is studying the association between automobile exhaust (E) and the prevalence of asthma in children (A). Other air pollutants (P) may also affect asthma prevalence. The presence of wind (W) affects the concentrations of both (E) and (P). A researcher is studying the association between experiencing childhood abuse (A) and the occurrence of depression (D) as an adult. She has reason to believe that alcohol consumption (C) may mediate the relationship between (A) and (D).State in words the meaning of the hazard ratios for self-rated health in model 1. Be sure to include information on statistical significance. (5 points)State in words the meaning of the hazard ratios for self-rated health in model 3. Discuss whether or not breast cancer stage and daily task limitations were confounders of the self-rated health/mortality association. Justify your response and state your overall conclusions based on the analyses. (15 points)Fill in the table below for columns A and B. The table shows different associations where Factors X and Z are being measured for their effect on an outcome. For each effect measure there are shown three results: a result with Factor X only (X+Z-), a result with Factor Z only (X-Z+), and the Observed Joint Effect for both factors (X+Z+). In column A, indicate whether the interaction is positive or negative, and in column B, indicate whether the interaction is additive or multiplicative. If no interaction is present, put “None” in columns A and B. (10 points)Imagine that you are conducting a randomized controlled trial comparing two medicines (Medicine 1 and Medicine 2) in the prevention of asthma attacks. The following table shows some of the characteristics of the study population for each group: Assessing Confounding in Multivariate Regression (20 points) A researcher studied women with breast cancer to better understand the association between self-rated health and breast cancer mortality (Prehn, 1996). By using survival analysis, the following results were obtained from three different models: Assessing and Interpreting Effect Modification (15 points) Effect Measure Effect of Factor X (X+ Z-) Effect of Factor Z (X- Z+) Observed Joint Effect (X+Z+) A Positive or negative? B Additive or multiplicative? Attributable Risk 20.0 / 1000 15.0 / 1000 60.0 / 1000 Positive Relative Risk 3.0 2.0 4.0 Relative Risk 2.0 3.0 6.0 Medicine 1 Group (n=100) Medicine 2 Group (n=100) Cigarette smoker Yes 30 10 No 70 90 Physically active Yes 35 35 No 65 65 Discuss how you would determine if there is confounding and/or effect modification by cigarette smoking or physical activity in your study. Include details of any strategies you would use and provide specific examples using these study data. (5 points) Reference: Prehn, A. W. (1996). Self-rated health in middle-aged and elderly women with breast cancer (Doctoral dissertation). Retrieved from Dissertation Abstracts International.