A new virus has taken root in a country. Government officials are reporting that 15% of the population is currently infected with the virus. However, epidemiologists across the country claim to be observing a much higher infection rate. It was found that 157 people out of a randomly selected sample of 1040 people from around the country were infected with the virus. Use the critical value method to determine if the sample data support the epidemiologists' supposition that the true rate of infection in the country is higher than 15%. Use a significance level of 5%. State the null and alternative hypothesis for this test. Ho: v H₁: ? Determine if this test is left-tailed, right-tailed, or two-tailed. Oright-tailed Otwo-tailed Oleft-tailed Should the standard normal (2) distribution or Student's (t) distribution be used for this test? The standard normal (2) distribution should be used O The Student's t distribution should be used Determine the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list. Determine the test statistic. Round the solution to two decimal places. 225 10000 125 1000
A new virus has taken root in a country. Government officials are reporting that 15% of the population is currently infected with the virus. However, epidemiologists across the country claim to be observing a much higher infection rate. It was found that 157 people out of a randomly selected sample of 1040 people from around the country were infected with the virus. Use the critical value method to determine if the sample data support the epidemiologists' supposition that the true rate of infection in the country is higher than 15%. Use a significance level of 5%. State the null and alternative hypothesis for this test. Ho: v H₁: ? Determine if this test is left-tailed, right-tailed, or two-tailed. Oright-tailed Otwo-tailed Oleft-tailed Should the standard normal (2) distribution or Student's (t) distribution be used for this test? The standard normal (2) distribution should be used O The Student's t distribution should be used Determine the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list. Determine the test statistic. Round the solution to two decimal places. 225 10000 125 1000
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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#33). This is 1 question. Need help with critical value and test statistic.
![### Hypothesis Testing: Virus Infection Rate
A new virus has taken root in a country. Government officials are reporting that 15% of the population is currently infected with the virus. However, epidemiologists across the country claim to be observing a much higher infection rate.
It was found that 157 people out of a randomly selected sample of 1040 people from around the country were infected with the virus.
**Objective:**
Use the critical value method to determine if the sample data support the epidemiologists' supposition that the true rate of infection in the country is higher than 15%. Use a significance level of 5%.
#### Steps to Follow:
1. **State the null and alternative hypothesis for this test.**
- Null Hypothesis (\(H_0\)): \(p \leq 0.15\)
- Alternative Hypothesis (\(H_1\)): \(p > 0.15\)
2. **Determine if this test is left-tailed, right-tailed, or two-tailed.**
- This is a right-tailed test because the alternative hypothesis is testing if the rate is higher than 15%.
3. **Should the standard normal (z) distribution or Student's (t) distribution be used for this test?**
- The standard normal (z) distribution should be used because we are testing proportions and the sample size is large (n = 1040).
4. **Determine the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places.**
- For a right-tailed test at a significance level of 5%, the critical value (z) is typically 1.645.
5. **Determine the test statistic. Round the solution to two decimal places.**
- First, calculate the sample proportion (\(\hat{p}\)):
\[
\hat{p} = \frac{157}{1040} \approx 0.151
\]
- Then calculate the test statistic (z):
\[
z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}
\]
Where \(p_0 = 0.15\) and \(n = 1040\).
\[
z = \frac{0.151 - 0.15}{\sqrt{\frac](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F090c748e-ae6e-4835-a77f-8d1d8bf06681%2F752b4efe-6349-4e56-86bf-7fc513dd1017%2Fdx74n9f8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing: Virus Infection Rate
A new virus has taken root in a country. Government officials are reporting that 15% of the population is currently infected with the virus. However, epidemiologists across the country claim to be observing a much higher infection rate.
It was found that 157 people out of a randomly selected sample of 1040 people from around the country were infected with the virus.
**Objective:**
Use the critical value method to determine if the sample data support the epidemiologists' supposition that the true rate of infection in the country is higher than 15%. Use a significance level of 5%.
#### Steps to Follow:
1. **State the null and alternative hypothesis for this test.**
- Null Hypothesis (\(H_0\)): \(p \leq 0.15\)
- Alternative Hypothesis (\(H_1\)): \(p > 0.15\)
2. **Determine if this test is left-tailed, right-tailed, or two-tailed.**
- This is a right-tailed test because the alternative hypothesis is testing if the rate is higher than 15%.
3. **Should the standard normal (z) distribution or Student's (t) distribution be used for this test?**
- The standard normal (z) distribution should be used because we are testing proportions and the sample size is large (n = 1040).
4. **Determine the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places.**
- For a right-tailed test at a significance level of 5%, the critical value (z) is typically 1.645.
5. **Determine the test statistic. Round the solution to two decimal places.**
- First, calculate the sample proportion (\(\hat{p}\)):
\[
\hat{p} = \frac{157}{1040} \approx 0.151
\]
- Then calculate the test statistic (z):
\[
z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}
\]
Where \(p_0 = 0.15\) and \(n = 1040\).
\[
z = \frac{0.151 - 0.15}{\sqrt{\frac
![### Hypothesis Testing Tutorial
This guide will help you execute a hypothesis test step by step. Follow the instructions and provide your answers in the appropriate sections.
**Step 1: Determine the type of test**
- Is the test left-tailed, right-tailed, or two-tailed?
- [ ] right-tailed
- [ ] two-tailed
- [ ] left-tailed
**Step 2: Choose the distribution**
- Should the standard normal (z) distribution or Student's (t) distribution be used for this test?
- [ ] The standard normal (z) distribution should be used
- [ ] The Student’s t distribution should be used
**Step 3: Determine critical value(s)**
- Calculate the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list.
*(Enter critical value(s) here)*
**Step 4: Calculate the test statistic**
- Determine the test statistic. Round the solution to two decimal places.
*(Enter test statistic here)*
**Step 5: Draw a conclusion**
- Based on your analysis and calculations, determine the appropriate conclusion for this hypothesis test.
- [ ] The sample data do not provide sufficient evidence to reject the government's claim (null hypothesis) that the infection rate of the virus is 15% and thus we conclude that the infection rate of the virus is likely 15%.
- [ ] The sample data provide sufficient evidence to reject the epidemiologists' claim (alternative hypothesis) that the infection rate is higher than 15% and thus we conclude that the infection rate of the virus is likely 15%.
- [ ] The sample data do not provide sufficient evidence to reject the epidemiologists' claim (alternative hypothesis) that the infection rate is higher than 15% and thus we concluded that the infection rate of the virus is likely greater than 15%.
- [ ] The sample data provide sufficient evidence to reject the government's claim (null hypothesis) that the infection rate of the virus is 15% and thus we conclude that the infection rate of the virus is likely greater than 15%.
For further guidance, refer to the detailed explanations and examples provided in our hypothesis testing module.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F090c748e-ae6e-4835-a77f-8d1d8bf06681%2F752b4efe-6349-4e56-86bf-7fc513dd1017%2Fb3817oj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing Tutorial
This guide will help you execute a hypothesis test step by step. Follow the instructions and provide your answers in the appropriate sections.
**Step 1: Determine the type of test**
- Is the test left-tailed, right-tailed, or two-tailed?
- [ ] right-tailed
- [ ] two-tailed
- [ ] left-tailed
**Step 2: Choose the distribution**
- Should the standard normal (z) distribution or Student's (t) distribution be used for this test?
- [ ] The standard normal (z) distribution should be used
- [ ] The Student’s t distribution should be used
**Step 3: Determine critical value(s)**
- Calculate the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list.
*(Enter critical value(s) here)*
**Step 4: Calculate the test statistic**
- Determine the test statistic. Round the solution to two decimal places.
*(Enter test statistic here)*
**Step 5: Draw a conclusion**
- Based on your analysis and calculations, determine the appropriate conclusion for this hypothesis test.
- [ ] The sample data do not provide sufficient evidence to reject the government's claim (null hypothesis) that the infection rate of the virus is 15% and thus we conclude that the infection rate of the virus is likely 15%.
- [ ] The sample data provide sufficient evidence to reject the epidemiologists' claim (alternative hypothesis) that the infection rate is higher than 15% and thus we conclude that the infection rate of the virus is likely 15%.
- [ ] The sample data do not provide sufficient evidence to reject the epidemiologists' claim (alternative hypothesis) that the infection rate is higher than 15% and thus we concluded that the infection rate of the virus is likely greater than 15%.
- [ ] The sample data provide sufficient evidence to reject the government's claim (null hypothesis) that the infection rate of the virus is 15% and thus we conclude that the infection rate of the virus is likely greater than 15%.
For further guidance, refer to the detailed explanations and examples provided in our hypothesis testing module.
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