COVID-19 (novel corona virus) took the world by surprise in late 2019. By early 2020, nearly all countries worldwide were affected. Early reports from the U.S. Centers for Disease Control and Prevention (CDC) estimated that approximately 18% of those infected with the corona virus were asymptomatic (showed no symptoms of the virus). The rate of asymptomatic infections is important, since such people can unwittingly spread the virus to those around them. Suppose that 21.6% of a recent sample of 415 infected individuals were found to be asymptomatic. Using a significance level of 2%, test the hypothesis that the proportion of all people infected with the corona virus and are asymptomatic is different than 18%. Use the p-value method. State the null and alternative hypothesis for this test. Ho:? H₁: ? ✓ Determine if this test is left-tailed, right-tailed, or two-tailed. O left-tailed O two-tailed Oright-tailed Should the standard normal (z) distribution or Student's (t) distribution be used for this test? The standard normal (2) distribution should be used 75°F H Partly cloudy
COVID-19 (novel corona virus) took the world by surprise in late 2019. By early 2020, nearly all countries worldwide were affected. Early reports from the U.S. Centers for Disease Control and Prevention (CDC) estimated that approximately 18% of those infected with the corona virus were asymptomatic (showed no symptoms of the virus). The rate of asymptomatic infections is important, since such people can unwittingly spread the virus to those around them. Suppose that 21.6% of a recent sample of 415 infected individuals were found to be asymptomatic. Using a significance level of 2%, test the hypothesis that the proportion of all people infected with the corona virus and are asymptomatic is different than 18%. Use the p-value method. State the null and alternative hypothesis for this test. Ho:? H₁: ? ✓ Determine if this test is left-tailed, right-tailed, or two-tailed. O left-tailed O two-tailed Oright-tailed Should the standard normal (z) distribution or Student's (t) distribution be used for this test? The standard normal (2) distribution should be used 75°F H Partly cloudy
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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Question
![### COVID-19 Asymptomatic Infection Study
**COVID-19 (novel coronavirus)** took the world by surprise in late 2019. By early 2020, nearly all countries worldwide were affected.
Early reports from the U.S. Centers for Disease Control and Prevention (CDC) estimated that approximately **18% of those infected** with the coronavirus were asymptomatic (showed no symptoms of the virus). The rate of asymptomatic infections is important, since such people can unwittingly spread the virus to those around them.
Suppose that **21.6% of a recent sample of 415 infected individuals** were found to be asymptomatic.
Using a significance level of **2%**, test the hypothesis that the proportion of all people infected with the coronavirus and asymptomatic is different from **18%**. Use the **p-value method**.
**State the null and alternative hypothesis for this test.**
\[ H_0: \, ? \]
\[ H_1: \, ? \]
**Determine if this test is left-tailed, right-tailed, or two-tailed.**
- left-tailed
- two-tailed [ ]
- right-tailed
**Should the standard normal (z) distribution or Student’s (t) distribution be used for this test?**
- The standard normal (z) distribution should be used [ ]
---
**Explanation of Diagrams and Graphs:**
1. **Hypothesis Notation:**
- \( H_0 \) and \( H_1 \) are placeholders that require completion to form the null and alternative hypotheses. In context, these will typically look like:
- \( H_0: p = 0.18 \) (the proportion of asymptomatic infections is 18%)
- \( H_1: p \neq 0.18 \) (the proportion of asymptomatic infections is different from 18%)
2. **Test Type Selection:**
- The question prompts for a determination of whether the statistical test should be one-tailed or two-tailed. Given that the question asks whether the proportion is different from 18%, it suggests a two-tailed test is appropriate.
3. **Distribution Selection:**
- It asks whether to use the standard normal (z) distribution or Student’s (t) distribution. For hypothesis tests concerning proportions, particularly with a large sample size (n = 415), we use the standard normal distribution (](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf14cf2c-4c6b-44b0-8c19-b82da3615fd0%2F490d2071-4943-4478-8521-c8088b036686%2F4crzpr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### COVID-19 Asymptomatic Infection Study
**COVID-19 (novel coronavirus)** took the world by surprise in late 2019. By early 2020, nearly all countries worldwide were affected.
Early reports from the U.S. Centers for Disease Control and Prevention (CDC) estimated that approximately **18% of those infected** with the coronavirus were asymptomatic (showed no symptoms of the virus). The rate of asymptomatic infections is important, since such people can unwittingly spread the virus to those around them.
Suppose that **21.6% of a recent sample of 415 infected individuals** were found to be asymptomatic.
Using a significance level of **2%**, test the hypothesis that the proportion of all people infected with the coronavirus and asymptomatic is different from **18%**. Use the **p-value method**.
**State the null and alternative hypothesis for this test.**
\[ H_0: \, ? \]
\[ H_1: \, ? \]
**Determine if this test is left-tailed, right-tailed, or two-tailed.**
- left-tailed
- two-tailed [ ]
- right-tailed
**Should the standard normal (z) distribution or Student’s (t) distribution be used for this test?**
- The standard normal (z) distribution should be used [ ]
---
**Explanation of Diagrams and Graphs:**
1. **Hypothesis Notation:**
- \( H_0 \) and \( H_1 \) are placeholders that require completion to form the null and alternative hypotheses. In context, these will typically look like:
- \( H_0: p = 0.18 \) (the proportion of asymptomatic infections is 18%)
- \( H_1: p \neq 0.18 \) (the proportion of asymptomatic infections is different from 18%)
2. **Test Type Selection:**
- The question prompts for a determination of whether the statistical test should be one-tailed or two-tailed. Given that the question asks whether the proportion is different from 18%, it suggests a two-tailed test is appropriate.
3. **Distribution Selection:**
- It asks whether to use the standard normal (z) distribution or Student’s (t) distribution. For hypothesis tests concerning proportions, particularly with a large sample size (n = 415), we use the standard normal distribution (
![### Hypothesis Testing Procedure
#### Student's t Distribution
- **The student's t distribution should be used.**
#### Determine the Test Statistic
- **Determine the test statistic for the hypothesis test. Round the solution to two decimal places.**
- [Text Box for Answer]
#### Determine the p-value
- **Determine the p-value for the hypothesis test. Round the solution to four decimal places.**
- [Text Box for Answer]
#### Conclusion for the Hypothesis Test
- **Determine the appropriate conclusion for this hypothesis test.**
1. **Option A:**
- The sample data provide sufficient evidence to reject the null hypothesis that the proportion of all people infected with the coronavirus and are asymptomatic is 0.18 and thus we conclude that the proportion of people that are infected with coronavirus and are asymptomatic is not equal to 0.18.
2. **Option B:**
- The sample data provide sufficient evidence to reject the alternative hypothesis that the proportion of all people who are infected with the coronavirus and are asymptomatic is different than 0.18 and thus we conclude that the proportion of people that are infected with coronavirus and are asymptomatic is likely equal to 0.18.
3. **Option C:**
- The sample data do not provide sufficient evidence to reject the null hypothesis that the proportion of all people infected with the coronavirus and are asymptomatic is 0.18 and thus we conclude that the proportion of people that are infected with coronavirus and are asymptomatic is likely equal to 0.18.
4. **Option D:**
- The sample data do not provide sufficient evidence to reject the alternative hypothesis that the proportion of all people who are infected with the coronavirus and are asymptomatic is different than 0.18 and thus we conclude that the proportion of people that are infected with coronavirus and are asymptomatic is likely not equal to 0.18.
Note: Ensure to select the appropriate conclusion based on the p-value and test statistic calculations.
### Additional Notes:
- This section guides you through performing a hypothesis test, determining the test statistic, calculating the p-value, and making an appropriate conclusion for hypotheses related to the proportion of people infected with the coronavirus who are asymptomatic.
- Understanding how to perform hypothesis tests correctly is essential in making data-driven decisions and drawing accurate conclusions based on sample data.
#### Weather Information
- 75°F, Partly](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf14cf2c-4c6b-44b0-8c19-b82da3615fd0%2F490d2071-4943-4478-8521-c8088b036686%2F2m38dqg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing Procedure
#### Student's t Distribution
- **The student's t distribution should be used.**
#### Determine the Test Statistic
- **Determine the test statistic for the hypothesis test. Round the solution to two decimal places.**
- [Text Box for Answer]
#### Determine the p-value
- **Determine the p-value for the hypothesis test. Round the solution to four decimal places.**
- [Text Box for Answer]
#### Conclusion for the Hypothesis Test
- **Determine the appropriate conclusion for this hypothesis test.**
1. **Option A:**
- The sample data provide sufficient evidence to reject the null hypothesis that the proportion of all people infected with the coronavirus and are asymptomatic is 0.18 and thus we conclude that the proportion of people that are infected with coronavirus and are asymptomatic is not equal to 0.18.
2. **Option B:**
- The sample data provide sufficient evidence to reject the alternative hypothesis that the proportion of all people who are infected with the coronavirus and are asymptomatic is different than 0.18 and thus we conclude that the proportion of people that are infected with coronavirus and are asymptomatic is likely equal to 0.18.
3. **Option C:**
- The sample data do not provide sufficient evidence to reject the null hypothesis that the proportion of all people infected with the coronavirus and are asymptomatic is 0.18 and thus we conclude that the proportion of people that are infected with coronavirus and are asymptomatic is likely equal to 0.18.
4. **Option D:**
- The sample data do not provide sufficient evidence to reject the alternative hypothesis that the proportion of all people who are infected with the coronavirus and are asymptomatic is different than 0.18 and thus we conclude that the proportion of people that are infected with coronavirus and are asymptomatic is likely not equal to 0.18.
Note: Ensure to select the appropriate conclusion based on the p-value and test statistic calculations.
### Additional Notes:
- This section guides you through performing a hypothesis test, determining the test statistic, calculating the p-value, and making an appropriate conclusion for hypotheses related to the proportion of people infected with the coronavirus who are asymptomatic.
- Understanding how to perform hypothesis tests correctly is essential in making data-driven decisions and drawing accurate conclusions based on sample data.
#### Weather Information
- 75°F, Partly
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