A survey of 200 senior citizens was undertaken and it was found that 26 of them had the flu vaccine this year. Do these data suggest that the proportion of senior citizens who get the flu vaccine is significantly less than 21 % ? Test at a = 0.10. Round your answers to three decimal places, and round any interim calculations to four decimal places. What is the test statistic?
A survey of 200 senior citizens was undertaken and it was found that 26 of them had the flu vaccine this year. Do these data suggest that the proportion of senior citizens who get the flu vaccine is significantly less than 21 % ? Test at a = 0.10. Round your answers to three decimal places, and round any interim calculations to four decimal places. What is the test statistic?
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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![**Statistical Test for Proportion of Senior Citizens Receiving the Flu Vaccine**
In a survey of 200 senior citizens, it was found that 26 had received the flu vaccine this year. This prompts the question: is the proportion of senior citizens who get the flu vaccine significantly less than 21%?
To answer this, we perform a hypothesis test at a significance level of \( \alpha = 0.10 \). It is important to ensure all answers are rounded to three decimal places, and any interim calculations are rounded to four decimal places.
**Hypothesis:**
- Null Hypothesis \( H_0 \): \( p = 0.21 \)
- Alternative Hypothesis \( H_a \): \( p < 0.21 \)
**Calculate the Test Statistic:**
To find the test statistic, use the formula for the test statistic of a proportion:
\[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \]
where:
- \( \hat{p} \) is the sample proportion (\(\hat{p} = \frac{26}{200}\)),
- \( p_0 \) is the population proportion (0.21),
- \( n \) is the sample size (200).
Plug these values into the formula, and round your final answer to three decimal places.
**Question:**
What is the test statistic?
\[ \boxed{\text{Enter your answer here}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2995aa7-eb9d-45f3-8f01-89ee9ae70a2c%2F261ee793-2797-4f18-a01b-b2bd71ac04da%2Fbnpbpdi_processed.png&w=3840&q=75)
Transcribed Image Text:**Statistical Test for Proportion of Senior Citizens Receiving the Flu Vaccine**
In a survey of 200 senior citizens, it was found that 26 had received the flu vaccine this year. This prompts the question: is the proportion of senior citizens who get the flu vaccine significantly less than 21%?
To answer this, we perform a hypothesis test at a significance level of \( \alpha = 0.10 \). It is important to ensure all answers are rounded to three decimal places, and any interim calculations are rounded to four decimal places.
**Hypothesis:**
- Null Hypothesis \( H_0 \): \( p = 0.21 \)
- Alternative Hypothesis \( H_a \): \( p < 0.21 \)
**Calculate the Test Statistic:**
To find the test statistic, use the formula for the test statistic of a proportion:
\[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \]
where:
- \( \hat{p} \) is the sample proportion (\(\hat{p} = \frac{26}{200}\)),
- \( p_0 \) is the population proportion (0.21),
- \( n \) is the sample size (200).
Plug these values into the formula, and round your final answer to three decimal places.
**Question:**
What is the test statistic?
\[ \boxed{\text{Enter your answer here}} \]
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