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Fizer (NOT Pfizer) is a pharmaceutical company which has developed a new vaccine for COVID-1 order to bring their vaccine to market, the FDA requires them to demonstrate the efficacy of th vaccine through clinical trials. With this aim, they conduct the following experiment. N = n + m participants are recruited randomized clinical trial.

Fizer (NOT Pfizer) is a pharmaceutical company which has developed a new vaccine for COVID-1 order to bring their vaccine to market, the FDA requires them to demonstrate the efficacy of th vaccine through clinical trials. With this aim, they conduct the following experiment. N = n + m participants are recruited randomized clinical trial.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
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Section2.5: Markov Chain
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Fizer (NOT Pfizer) is a pharmaceutical company which has developed a new vaccine for COVID-19. In order to bring their vaccine to market, the FDA requires them to demonstrate the efficacy of their vaccine through clinical trials. With this aim, they conduct the following experiment. N = n + m participants are recruited for a randomized clinical trial. • A subset of n subjects are assigned to the experiment group and receive the real vaccine • And m subjects are assigned to the control group to whom a fake placebo is administered. At a later time, a survey is conducted to see how many of the N = n + m subjects got COVID-19. Let X1, X2,..., Xn 72 iid Ber(0x) be 1/0 variables representing whether each of the n subjects in the experiment group had or didn't have COVID (respectively). Similarly, let Y₁, Y2,..., Ymid Ber(0y) 1. be 1/0 variables for the m subjects in the control group. Describe the interpretation for 0x and Oy. What is the interpretation for Oy - Ox? 2. Let denote 0 = 0y - Ox. What is the maximum likelihood estimator MLE for ? Compute Var (ÔMLE). 3. Using your answer from part (3) and using the central limit theorem for maximum likelihood estimators, derive the sampling distribution for OMLE 4. In class we saw that there are several ways of constructing a confidence interval, e.g., two-sided, left one-sided, right one-sided, etc. If you were part of the FDA overseeing this clinical trial; given a confidence level o, what type of a confidence interval would you like Fizer to report to give in order to give you an idea of the vaccine's efficacy? What is the interpretation for this sort of a confidence interval?
Transcribed Image Text:Fizer (NOT Pfizer) is a pharmaceutical company which has developed a new vaccine for COVID-19. In order to bring their vaccine to market, the FDA requires them to demonstrate the efficacy of their vaccine through clinical trials. With this aim, they conduct the following experiment. N = n + m participants are recruited for a randomized clinical trial. • A subset of n subjects are assigned to the experiment group and receive the real vaccine • And m subjects are assigned to the control group to whom a fake placebo is administered. At a later time, a survey is conducted to see how many of the N = n + m subjects got COVID-19. Let X1, X2,..., Xn 72 iid Ber(0x) be 1/0 variables representing whether each of the n subjects in the experiment group had or didn't have COVID (respectively). Similarly, let Y₁, Y2,..., Ymid Ber(0y) 1. be 1/0 variables for the m subjects in the control group. Describe the interpretation for 0x and Oy. What is the interpretation for Oy - Ox? 2. Let denote 0 = 0y - Ox. What is the maximum likelihood estimator MLE for ? Compute Var (ÔMLE). 3. Using your answer from part (3) and using the central limit theorem for maximum likelihood estimators, derive the sampling distribution for OMLE 4. In class we saw that there are several ways of constructing a confidence interval, e.g., two-sided, left one-sided, right one-sided, etc. If you were part of the FDA overseeing this clinical trial; given a confidence level o, what type of a confidence interval would you like Fizer to report to give in order to give you an idea of the vaccine's efficacy? What is the interpretation for this sort of a confidence interval?
5. Using your answer from parts (3) and (4), derive the expression for the confidence interval at level (1-x), i.e., find land usuch that CI(0; α) = [la, ¹a]. 6. The code below contains a snippet for constructing a confidence interval. Complete the code for la and uso that the output of the cell is your confidence interval from part (5) at level a = 0.05. What do you conclude from your answer?
Transcribed Image Text:5. Using your answer from parts (3) and (4), derive the expression for the confidence interval at level (1-x), i.e., find land usuch that CI(0; α) = [la, ¹a]. 6. The code below contains a snippet for constructing a confidence interval. Complete the code for la and uso that the output of the cell is your confidence interval from part (5) at level a = 0.05. What do you conclude from your answer?
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