5. A group of doctors are conducting a clinical trial for an experimental cancer drug. The graph below shows theprobability of patient survival as a function of time, t (in months). The functions for Streated (survival probabilityof patients treated by the drug) and Splacebo (survival probability of patients given a placebo) are determined tobe: Streated(t) = e-(15)" and Splacebo (t) = e15t144.(a)"Ise the given function15tPpiacevo \"e-144to calculate%3DSpreatedthe average survival probability ofthe placebo group for the first 10months of the study. Round to 2decimal places.5-0:8-0:6Splacebo-0:40:21020(b)The efficacy of the drug at any timer > 0 can be defined as E(T) = | (Streated(t) – Splacebo (t)) dt.Note: This can be thought of as representing a difference of areas.Use a Riemann sum with 5 sub-intervals of equal width to approximate E(10). Use right endpoints. Roundyour final answer to 2 decimal places.(c)the first T months). Is the drug beneficial atA drug is beneficial if E(T) > 0 (meaning treated subjects have a larger average survival time overmonths? (Aone-sentence answer is enough.)(d)Is the drug beneficial at T = 20? Explain in 1 or 2 sentences.Survival probability

Given that Streatedt=e−t122Splacebot=e−15t144

Answered: A group of doctors are conducting a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In a study of the lung function of children, the volume of air exhaled under force in one second is called FEV1. (FEV1 stands for forced expiratory volume in one second.) Measurements were made on a group of children each year for two years. A linear model was fit to predict this year’s FEV1 as a function of last year’s FEV1 (in liters), the child’s gender (0 = Male, 1 = Female), the child’s height (in m), and the ambient atmospheric pressure (in mm). To try to improve the prediction of FEV1, additional independent variables are included in the model. These new variables are Weight (in kg), the product (interaction) of Height and Weight, and the ambient temperature (in °C). The following MINITAB output presents results of fitting the model FEV1 = β0 + β1 Last FEV1 + β2 Gender + β3 Height + β4 Weight + β5 Height · Weight + β6 Temperature + β7 Pressure + ε a) The F statistic is? b) How many degrees of freedom does the F statistic have? c) Find the P-value for the F statistic. Is the…

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