Answered: We have a sample of 2,400 geriatric…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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We have a sample of 2,400 geriatric patients who are in an assisted living home, of which 1,200 participated in a new preventative Drug A. Rates of UTIs tend to be higher than average among this population. As part of a preventative and treatment intervention, we are examining the performance of several drugs: Preventative Drug (before the onset of UTI) Drug A: preventative UTI drug taken daily in hopes to prevent the growth of bacteria that causes UTIs Treatment Drugs (after the onset of UTI) Drug B: New antibiotic for treating UTIs Drug C: Conventional antibiotic for treating UTIs Information for how many patients took each drug or combination of drugs is summarized below in the two tables. Use these to answer questions a) -d) Table 1. Summary of performance of drug A: UTI rates among those taking and not taking drug A Did not take Drug A Did take Drug A Total UTI 759 887 1646 No UTI 441 312 753 Total 1200 1200 2400 Table 2. Summary of performance of drug B and C: recovery status after 1 week of taking medications. Did not take Drug A Did take Drug A Drug B Drug C Drug B Drug C Recovered 191 209 221 244 Not Recovered 189 170 223 199 Total 380 379 444 443 a) Use the above Table 1 to determine if Drug A was useful in preventing UTIs. In other words, is the proportion of those having taking Drug A but still getting a UTI equal to average rate of UTI for this population (living in an assisted living home) of 74%. Use hypothesis testing to test our hypothesis and use the confidence interval approach with a significance level of α=0.01. b) Using Table 2, let’s examine the rate of UTI recovery among Drug C (conventional antibiotics). The manufacturer of Drug C claims it has a success rate (recovery within a week) of 55%. Use our data to see if this success rate is true: test if our recovery rate of those taking Drug C, regardless of whether the person took Drug A or not, is the same or different than 55%. Use hypothesis testing and the p-value approach with an α=0.05. c) Similarly, let’s examine Drug B’s performance. Repeat our hypothesis among Drug B: test if our recovery rate of those taking drug B is different than 55% (regardless of whether the patient took Drug A or not). Use hypothesis testing and p-value approach with an α=0.1.

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