Find the probability the sum is 5 or smaller, rounded to three decimal places. The test will take an answer within 0.001

Given the apportionment as in Question 29-31, if a 16th teacher is to be assigned to a school, what school should receive the teacher using the Huntington-Hill method?

Find the Banzhaf Power Index of the voter with weight 4.  The test will take an answer within 0.01.  

Find the probability the sum is even, given that that sum is 9 or larger. The test will take an answer within 0.001

Using Jefferson’s method to appropriate the 15 teachers, how many teachers will Washington get?  

Question 1h: The authors note several limitations of their study. One of them is that they were limited to using only variables that were recorded in the THIN medical database that they used for their analyses. As such, prescriptions that individuals received “out-of-system” would not have been captured in the database. What is the type of bias that we would be concerned about due to this? Briefly explain your reasoning (1-2 sentences). 

Question 1e: Now, for the measure of association you calculated in Question 1c, calculate the accompanying 95% confidence interval. Show your calculations in the free-text space provided. Use four decimal places during calculations (i.e., 0.0000), but round all final answers to two decimal places (i.e., 0.00). 

Study Design (Modified) Initiation of either metformin use or sulfonylurea use was defined as not having a history of use of either medication before entering the study and refilling at least 1 prescription within 60 days after the end of the supply of the first prescription (30). The date of the first refill was denoted as the index date. We did not exclude the patients with type 2 diabetes who used other types of antidiabetic medication before the first prescription of either metformin or a sulfonylurea. Because metformin is contraindicated for patients with severe chronic kidney disease (31), we excluded persons with severe chronic kidney disease (30), defined as an estimated glomerular filtration rate less than 30 mL/minute/1.73 m2 on at least 2 occasions more than 90 days apart or at least 1 Read code for advanced chronic kidney disease (32). In addition, we also excluded persons who had a history of VTE before the index date or who had no general practitioner visit or specialist referral within 1 year before the index date. Assessment of outcomes (Modified) The primary outcome of interest was a diagnosis of incident VTE (the combined endpoint of PE and DVT), with secondary outcomes of PE and DVT separately. An individual was considered to have developed the outcome of interest if he or she had a recorded Read code of PE or DVT and received anticoagulant treatment (36). Since VTE is potentially fatal and some individuals might have died before receiving an anticoagulant, we also considered participants to have developed VTE if they died within 1 month after a recorded code of PE or DVT but without a prescription for an anticoagulant or autopsy results (37). Note: Read codes are a thesaurus of terms, synonyms, and abbreviations used in medical practice in the UK and can be mapped on to ICD-10 codes. Results (Modified) Table 1 Metformin Sulfonylurea Total VTE 555 75 630 No VTE 116,917 13,760 130,677 Total 117,472 13,835 131,307 Question 1c: Using data from Table 1, calculate the appropriate crude relative measure of association comparing VTE among those using metformin and those using sulfonylurea. Show your formula in the free-text space provided. Round your final answer to two decimal places (0.00). 

Sha, T., Zhang, Y., Li, C., Lei, G., Wu, J., Li, X., Yang, Z., Zeng, C. and Wei, J., 2022. Association of metformin use with risk of venous thromboembolism in adults with type 2 diabetes: a general-population–based cohort study. American Journal of Epidemiology, 191(5), pp.856-866. Study Abstract (Modified) Metformin is hypothesized to protect against the risk of venous thromboembolism (VTE); however, there is a paucity of data supporting this hypothesis. Among individuals aged 40–90 years with a diagnosis of type 2 diabetes in the Health Improvement Network database (2000–2019), we compared [outcomes of] VTE, pulmonary embolism, and deep vein thrombosis among metformin initiators with those among sulfonylurea initiators. Individuals were followed from their first prescription refill to an incident VTE, drug discontinuation, switching or augmenting, plan disenrollment, or the end of the study, whichever occurred first… Question 1a: What was the purpose of the study conducted by Sha et al?

Wu, K., Feskanich, D., Fuchs, C.S., Willett, W.C., Hollis, B.W. and Giovannucci, E.L., 2007. A nested case–control study of plasma 25-hydroxyvitamin D concentrations and risk of colorectal cancer. Journal of the National Cancer Institute, 99(14), pp.1120-1129. Study Purpose and Design (Modified): Wu et al conducted a study to investigate the relationship between low vitamin D status (25-hydroxyvitamin D level 90%) were confirmed through medical records; the remaining cases were confirmed by corroborating information on cancer diagnosis from participants (i.e., through consent forms sent by participants). Participants without cancer were identified by the year (same year) and month (within 1 month) of blood donation. Results (Modified) Vitamin D Status Colorectal Cancer No Colorectal Cancer Total Deficient 103 167 270 Not Deficient 76 189 265 Total 179 356 535 Question 2a. Calculate the appropriate relative measure of association for this study comparing those who are not vitamin D deficient (exposed) to those who are vitamin D deficient (unexposed). Show your calculations in the free-text space provided. Round your final answer to two decimal places (i.e., 0.00).