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Determine the test statistic for the hypothesis test. Round the solution to two decimal places. Determine the p-value for the hypothesis test. Round the solution to four decimal places. Determine the appropriate conclusion for this hypothesis test. O The sample data provide sufficient evidence to reject the null hypothesis that the proportion of all people infected with the corona virus and are asymptomatic is 0.18 and thus we conclude that the proportion of people that are infected with corona virus and are asymptomatic is not equal to 0.18. O The sample data provide sufficient evidence to reject the alternative hypothesis that the proportion of all people who are infected with the corona virus and are asymptomatic is different than 0.18 and thus we conclude that the proportion of people that are infected with corona virus and are asymptomatic is likely equal to 0.18. O The sample data do not provide sufficient evidence to reject the null hypothesis that the proportion of all people infected with the corona virus and are asymptomatic is 0.18 and thus we conclude that the proportion of people that are infected with corona virus and are asymptomatic is likely equal to 0.18.

Determine the test statistic for the hypothesis test. Round the solution to two decimal places. Determine the p-value for the hypothesis test. Round the solution to four decimal places. Determine the appropriate conclusion for this hypothesis test. O The sample data provide sufficient evidence to reject the null hypothesis that the proportion of all people infected with the corona virus and are asymptomatic is 0.18 and thus we conclude that the proportion of people that are infected with corona virus and are asymptomatic is not equal to 0.18. O The sample data provide sufficient evidence to reject the alternative hypothesis that the proportion of all people who are infected with the corona virus and are asymptomatic is different than 0.18 and thus we conclude that the proportion of people that are infected with corona virus and are asymptomatic is likely equal to 0.18. O The sample data do not provide sufficient evidence to reject the null hypothesis that the proportion of all people infected with the corona virus and are asymptomatic is 0.18 and thus we conclude that the proportion of people that are infected with corona virus and are asymptomatic is likely equal to 0.18.

MATLAB: An Introduction with Applications
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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### Understanding Asymptomatic COVID-19 Infection Rates: A Statistical Approach **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 are asymptomatic is different from 18%. Use the _p-value_ method. **State the null and alternative hypothesis for this test:** \[ H_0: p = 0.18 \] \[ H_1: p \neq 0.18 \] **Determine if this test is left-tailed, right-tailed, or two-tailed:** - ☐ left-tailed - ☑ right-tailed - ☑ two-tailed (Note for clarity: Although there are options provided next to "left-tailed", the correct choice cannot be determined with certainty based on the provided image.) ### Explanation of Terms: - **Null Hypothesis (H₀)**: This is a statement of no effect or no difference, and it is what we are trying to test. In this context, it states that the proportion of asymptomatic cases (p) is 18%. - **Alternative Hypothesis (H₁)**: This is what you aim to demonstrate to be true. It states that the proportion of asymptomatic cases (p) is not equal to 18%. - **Two-tailed Test**: A test where the area of interest is in both tails of the distribution. This is appropriate when you are looking for a difference in either direction, rather than a specific direction. ### Visual Aid: No graphs or diagrams are included in the provided image, but the text involves basic statistical hypothesis testing. ### Additional Information: - **Significance Level (α)**: The probability of rejecting the null hypothesis when it is actually true. A significance level of 2% (or 0.02) is used in this scenario. - **p-value Method
Transcribed Image Text:### Understanding Asymptomatic COVID-19 Infection Rates: A Statistical Approach **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 are asymptomatic is different from 18%. Use the _p-value_ method. **State the null and alternative hypothesis for this test:** \[ H_0: p = 0.18 \] \[ H_1: p \neq 0.18 \] **Determine if this test is left-tailed, right-tailed, or two-tailed:** - ☐ left-tailed - ☑ right-tailed - ☑ two-tailed (Note for clarity: Although there are options provided next to "left-tailed", the correct choice cannot be determined with certainty based on the provided image.) ### Explanation of Terms: - **Null Hypothesis (H₀)**: This is a statement of no effect or no difference, and it is what we are trying to test. In this context, it states that the proportion of asymptomatic cases (p) is 18%. - **Alternative Hypothesis (H₁)**: This is what you aim to demonstrate to be true. It states that the proportion of asymptomatic cases (p) is not equal to 18%. - **Two-tailed Test**: A test where the area of interest is in both tails of the distribution. This is appropriate when you are looking for a difference in either direction, rather than a specific direction. ### Visual Aid: No graphs or diagrams are included in the provided image, but the text involves basic statistical hypothesis testing. ### Additional Information: - **Significance Level (α)**: The probability of rejecting the null hypothesis when it is actually true. A significance level of 2% (or 0.02) is used in this scenario. - **p-value Method
### Hypothesis Testing in Statistics When performing hypothesis testing, especially in the context of understanding proportions within a population, there are several critical steps involved: determining the test statistic, calculating the p-value, and drawing a conclusion based on these calculations. #### Determine the Test Statistic for the Hypothesis Test *Round the solution to two decimal places.* ``` ______________________________________________________ ``` #### Determine the \( p \)-value for the Hypothesis Test *Round the solution to four decimal places.* ``` ______________________________________________________ ``` ### Drawing Conclusions from Sample Data Based on the analysis of the hypothesis test, select the most appropriate conclusion: - **Option 1:** > 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. - **Option 2:** > 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 from 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. - **Option 3:** > 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. ### Explanation of Concepts **Test Statistic:** The test statistic is a standardized value that is calculated from sample data during a hypothesis test. This value is used to determine whether to reject the null hypothesis. **\( p \)-value:** The \( p \)-value represents the probability of obtaining the observed results, or more extreme results, assuming that the null hypothesis is true. A small \( p \)-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis. **Conclusion:** Selecting the appropriate conclusion involves comparing the test statistic and the \( p \)-value to determine whether there is sufficient evidence to support the hypothesis that you are testing. In this context, options provided suggest various conclusions based on the evidence from the sample data. ### Weather Information The current weather is **75°F** and **
Transcribed Image Text:### Hypothesis Testing in Statistics When performing hypothesis testing, especially in the context of understanding proportions within a population, there are several critical steps involved: determining the test statistic, calculating the p-value, and drawing a conclusion based on these calculations. #### Determine the Test Statistic for the Hypothesis Test *Round the solution to two decimal places.* ``` ______________________________________________________ ``` #### Determine the \( p \)-value for the Hypothesis Test *Round the solution to four decimal places.* ``` ______________________________________________________ ``` ### Drawing Conclusions from Sample Data Based on the analysis of the hypothesis test, select the most appropriate conclusion: - **Option 1:** > 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. - **Option 2:** > 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 from 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. - **Option 3:** > 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. ### Explanation of Concepts **Test Statistic:** The test statistic is a standardized value that is calculated from sample data during a hypothesis test. This value is used to determine whether to reject the null hypothesis. **\( p \)-value:** The \( p \)-value represents the probability of obtaining the observed results, or more extreme results, assuming that the null hypothesis is true. A small \( p \)-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis. **Conclusion:** Selecting the appropriate conclusion involves comparing the test statistic and the \( p \)-value to determine whether there is sufficient evidence to support the hypothesis that you are testing. In this context, options provided suggest various conclusions based on the evidence from the sample data. ### Weather Information The current weather is **75°F** and **
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