ter 7 Zamba Week 11 Homework This homework assignment will be due exactly one week from the start of your discussion section during the week beginning April 3rd, 2023. For this homework assignment you may discuss with each other, however your final write-up must be completed independently. You may write your answers up on this question sheet, or on regular letter-sized paper, and scan to pdf. Given the mathematical notation to be used, use of Microsoft Word is discouraged. If you do use Word please save as a pdf to upload. Upload you homework to ICON as a single document. Grading: This assignment is worth 20 points; 2 points per question unless noted otherwise. A case-control study was conducted to identify reasons for the exceptionally high rate of lung cancer among male residents of coastal Georgia. The primary risk factor under investigation was employment in shipyards during World War II. To avoid potential confounding with smoking status we will analyze the data obtained from the smokers only. (We will be discussing confound- ing next week). Data for smokers Shipbuilding Cases Controls Yes No 94 51 315 273 When applicable: calculate answers to four decimal places; define notation you create; and use appropriate general notation. 1) What is the defining difference between cases and controls? 2) What proportion of cases were exposed to shipbuilding? Define and use appropriate tation. no- 3) Calculate the estimated standard error of the estimate calculated in question 2? Define and use appropriate notation. 4) Calculate a 95% confidence interval for the estimate calculated in question 2? 5) (1 point) Based on the confidence interval calculated in question 4, would you claim that the proportion of cases exposed to shipbuilding was statistically significantly different to 0.28? Explain your decision. 6) (1 point) Based on the confidence interval calculated in question 4, would you claim that the proportion of cases exposed to shipbuilding was statistically significantly different to 0.20? Explain your decision. 7) Calculate the test statistic for a two-sided hypothesis test, at the 5% level, to determine if the proportion of cases that were exposed to shipbuilding significantly differs from 0.16. Formally define your null and alternative hypotheses, and define and use appropriate notation. 8) (1 point) Is your test statistic calculated in question 7 statistically significant or not? Ex- plain your decision. 9) State the conclusion of your result of questions 7 and 8 in a complete stand-alone sentence. If statistically significant be sure to note the direction of the result. 10) Calculate the test statistic for a two-sided hypothesis test, at the 5% level, to determine if the proportion of cases that were exposed to shipbuilding significantly differs between cases and controls. Formally define your null and alternative hypotheses, and define and use appropriate notation. 11) (1 point) Is your test statistic calculated in question 10 statistically significant or not? Explain your decision. 12) State the conclusion of your result of questions 10 and 11 in a complete stand-alone sen- tence. If statistically significant be sure to note the direction of of the result.