receiving 200 mg of a newly-developed influenza vaccine who go on to contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's influenza vaccine who contract influenza strain X. Of 320 patients who are given last year's vaccine, 114 contract influenza strain X. Of 350 patients who are given the new vaccine 112 of them contract influenza strain X. Let PN be the proportion of patients receiving the newly-developed vaccine and pL be the proportion of patients receiving last year's vaccine. State the null and alternative hypotheses and the value of the tes statistic. Ho: PN = PL versus HA: PN > PL; Test statistic: Z = 0.99 Ho: PN = PL versus HA: PN > PL; Test statistic: Z = 1.55
receiving 200 mg of a newly-developed influenza vaccine who go on to contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's influenza vaccine who contract influenza strain X. Of 320 patients who are given last year's vaccine, 114 contract influenza strain X. Of 350 patients who are given the new vaccine 112 of them contract influenza strain X. Let PN be the proportion of patients receiving the newly-developed vaccine and pL be the proportion of patients receiving last year's vaccine. State the null and alternative hypotheses and the value of the tes statistic. Ho: PN = PL versus HA: PN > PL; Test statistic: Z = 0.99 Ho: PN = PL versus HA: PN > PL; Test statistic: Z = 1.55
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![### Hypothesis Testing in Medical Research: Vaccine Effectiveness against Influenza Strain X
#### Problem Statement
A 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 Formulation
We 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 Answers
Students 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7e444e2-a441-4a28-bca8-26e04764874a%2Fdb8c8839-7355-403d-86fe-5f92b68e289d%2F3jqkjk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing in Medical Research: Vaccine Effectiveness against Influenza Strain X
#### Problem Statement
A 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 Formulation
We 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 Answers
Students 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
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