### Hypothesis Testing in Medical Research: Vaccine Effectiveness against Influenza Strain X#### Problem StatementA medical researcher is studying the effectiveness of a newly-developed influenza vaccine compared to last year's vaccine. The researcher’s claim is that the proportion of patients receiving 200 mg of the new vaccine who contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's vaccine who contract the same strain.#### Data Collection- **Last Year's Vaccine:** Out of 320 patients, 114 contract influenza strain X.- **New Vaccine:** Out of 350 patients, 112 contract influenza strain X. The task is to define the proportion of patients contracting influenza X when using each vaccine. Let:- \( p_N \) be the proportion of patients receiving the new vaccine who contract influenza strain X.- \( p_L \) be the proportion of patients receiving last year's vaccine who contract influenza strain X.#### Hypothesis FormulationWe need to state the null and alternative hypotheses and determine the value of the test statistic.1. **Null Hypothesis (H₀)**: The proportions of patients contracting influenza strain X are the same for both vaccines. \[ \text{H₀: } p_N = p_L \]2. **Alternative Hypothesis (Hₐ)**: The proportion of patients contracting influenza strain X is less for the new vaccine compared to last year's vaccine. \[ \text{Hₐ: } p_N < p_L \]3. **Test Statistic Calculation and Analysis** Using the collected data and appropriate statistical tests: \[ \text{Test Statistic (Z) = 0.99} \]#### Possible Outcomes from Multiple-Choice AnswersStudents are presented with multiple choices to state the null and alternative hypotheses with corresponding test statistics:1. **Choice 1:** \[ \text{H₀: } p_N = p_L \text{ versus Hₐ: } p_N > p_L; \text{ Test statistic: } Z = 0.99 \]2. **Choice 2:** \[ \text{H₀: } p_N = p_L \text{ versus Hₐ: } p_N = p_L; \text{ Test statistic: } Z = 1.55 \]3. **Choice 3

According to the given information in this questionWe need to identify null and alternative…

Answered: receiving 200 mg of a newly-developed…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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