4. Two STT200 students, Don Diego and Elena Montero, want to estimate the population proportion of Democrats who wear a mask to help prevent the spread of COVID-19 at 90% confidence with a margin of error no more than 1.28%. How many Democrats would they need to survey to do this? Use the data above as a preliminary sample. n = 5. Suppose you conduct new survey this month and construct a 90% confidence interval for the population proportion of Americans who wear a mask to help prevent the spread of COVID-19 to be (0.883, 0.897). Which of the statements below is a correct interpretation of this confidence interval? OA. There is a 90% chance that about 89% of Americans wear a mask to help prevent the spread of COVID-19. OB. We can be 90% confident that the population proportion of Americans who wear a mask to help prevent the spread of COVID-19 is contained in the interval we constructed. OC. If we collected another random sample of the same size, there is a 90% chance that the new sample proportion will be between 0.883 and 0.897. OD. 90% of the time, the population proportion of Americans who wear a mask to help prevent the spread of COVID-19 is between 0.883 and 0.897.
4. Two STT200 students, Don Diego and Elena Montero, want to estimate the population proportion of Democrats who wear a mask to help prevent the spread of COVID-19 at 90% confidence with a margin of error no more than 1.28%. How many Democrats would they need to survey to do this? Use the data above as a preliminary sample. n = 5. Suppose you conduct new survey this month and construct a 90% confidence interval for the population proportion of Americans who wear a mask to help prevent the spread of COVID-19 to be (0.883, 0.897). Which of the statements below is a correct interpretation of this confidence interval? OA. There is a 90% chance that about 89% of Americans wear a mask to help prevent the spread of COVID-19. OB. We can be 90% confident that the population proportion of Americans who wear a mask to help prevent the spread of COVID-19 is contained in the interval we constructed. OC. If we collected another random sample of the same size, there is a 90% chance that the new sample proportion will be between 0.883 and 0.897. OD. 90% of the time, the population proportion of Americans who wear a mask to help prevent the spread of COVID-19 is between 0.883 and 0.897.
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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I need help with 4 and 5.
![### Analyzing Mask Usage Across Political Affiliations During COVID-19
**Introduction:**
In light of evidence about how COVID-19 spreads, the CDC recommends that people wear a cloth facemask to cover their nose and mouth in the community setting. The following information is adapted from the National Panel Study of COVID-19 by Vargas et al. A key finding of this study is: "Whether or not an American wears a facemask in public probably has a lot to do with their political affiliation". Results consistent with the survey conducted between April 14 and April 21, 2020, are summarized in the table below:
#### Table: Mask Usage by Political Affiliation
| | Masked | Unmasked | Total |
|----------------|--------|----------|-------|
| **Democrats** | 829 | 309 | 1138 |
| **Republicans**| 640 | 445 | 1085 |
**Instructions:**
- Round all calculated values in this problem to 4 decimal places.
#### Questions:
1. **Provide a Point Estimate for Population Proportion:**
- What is the population proportion of Democrats who wore a mask to help prevent the spread of COVID-19 at the time of the survey?
\( \hat{p} = \) __[Input Answer]__
2. **Construct a 90% Confidence Interval:**
- Construct a 90% confidence interval for the population proportion of Democrats who wore a mask to help prevent the spread of COVID-19 at the time of the survey.
\( ( \) __[Input Answer]__ \( , \) __[Input Answer]__ \( ) \)
3. **Conditions for Valid Confidence Interval:**
- Which of the following conditions must be met for the confidence interval to be valid? Select all that apply.
- [ ] A. The observations must be independent of one another.
- [ ] B. There must be at least 10 'success' and 10 'failure' observations.
- [ ] C. The sample size must be at least 30 or the population data must be normally distributed.
- [ ] D. There must be an expected count of at least 5 in every cell of the table.
This exercise aims to help you understand statistical inference and how to apply it to real-world data, particularly in the context of public health recommendations and behavioral responses during a global](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9896e9f0-21a4-41f5-9cfe-a9d2b9678883%2F66ae0e38-bd02-4ce2-bfb7-149571391b95%2Fg3qdtu_processed.png&w=3840&q=75)
Transcribed Image Text:### Analyzing Mask Usage Across Political Affiliations During COVID-19
**Introduction:**
In light of evidence about how COVID-19 spreads, the CDC recommends that people wear a cloth facemask to cover their nose and mouth in the community setting. The following information is adapted from the National Panel Study of COVID-19 by Vargas et al. A key finding of this study is: "Whether or not an American wears a facemask in public probably has a lot to do with their political affiliation". Results consistent with the survey conducted between April 14 and April 21, 2020, are summarized in the table below:
#### Table: Mask Usage by Political Affiliation
| | Masked | Unmasked | Total |
|----------------|--------|----------|-------|
| **Democrats** | 829 | 309 | 1138 |
| **Republicans**| 640 | 445 | 1085 |
**Instructions:**
- Round all calculated values in this problem to 4 decimal places.
#### Questions:
1. **Provide a Point Estimate for Population Proportion:**
- What is the population proportion of Democrats who wore a mask to help prevent the spread of COVID-19 at the time of the survey?
\( \hat{p} = \) __[Input Answer]__
2. **Construct a 90% Confidence Interval:**
- Construct a 90% confidence interval for the population proportion of Democrats who wore a mask to help prevent the spread of COVID-19 at the time of the survey.
\( ( \) __[Input Answer]__ \( , \) __[Input Answer]__ \( ) \)
3. **Conditions for Valid Confidence Interval:**
- Which of the following conditions must be met for the confidence interval to be valid? Select all that apply.
- [ ] A. The observations must be independent of one another.
- [ ] B. There must be at least 10 'success' and 10 'failure' observations.
- [ ] C. The sample size must be at least 30 or the population data must be normally distributed.
- [ ] D. There must be an expected count of at least 5 in every cell of the table.
This exercise aims to help you understand statistical inference and how to apply it to real-world data, particularly in the context of public health recommendations and behavioral responses during a global
![### Confidence Intervals and Sample Size Calculation
#### Example Scenario:
Two STT200 students, Don Diego and Elena Montero, want to estimate the population proportion of Democrats who wear a mask to help prevent the spread of COVID-19 at 90% confidence with a margin of error no more than 1.28%. How many Democrats would they need to survey to do this? Use the data above as a preliminary sample.
\[n = \text{____}\]
#### Understanding Confidence Intervals:
Suppose you conduct a new survey this month and construct a 90% confidence interval for the population proportion of Americans who wear a mask to help prevent the spread of COVID-19 to be (0.883, 0.897). Which of the statements below is a correct interpretation of this confidence interval?
- **A.** There is a 90% chance that about 89% of Americans wear a mask to help prevent the spread of COVID-19.
- **B.** We can be 90% confident that the population proportion of Americans who wear a mask to help prevent the spread of COVID-19 is contained in the interval we constructed.
- **C.** If we collected another random sample of the same size, there is a 90% chance that the new sample proportion will be between 0.883 and 0.897.
- **D.** 90% of the time, the population proportion of Americans who wear a mask to help prevent the spread of COVID-19 is between 0.883 and 0.897.
### Detailed Graphical Explanation
There is no graph or diagram provided in the image above. However, understanding confidence intervals typically involves visualizing:
1. **The Sample Proportion:** This is the point estimate derived from your survey data.
2. **The Margin of Error:** This represents the range around the sample proportion that could likely contain the true population proportion.
3. **The Confidence Level:** This informs us about the probability (in percentage terms) that the confidence interval contains the true population proportion if we were to repeat the survey multiple times.
### Key Points to Note:
- **Sample Size Calculation:** To determine how many individuals Don Diego and Elena need to survey, use the formula for sample size in proportion estimation considering the desired margin of error and confidence level.
- **Correct Interpretation (Question 5):** The correct interpretation of a confidence interval is covered in statement **B**. This means we can](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9896e9f0-21a4-41f5-9cfe-a9d2b9678883%2F66ae0e38-bd02-4ce2-bfb7-149571391b95%2Fa5vx0is_processed.png&w=3840&q=75)
Transcribed Image Text:### Confidence Intervals and Sample Size Calculation
#### Example Scenario:
Two STT200 students, Don Diego and Elena Montero, want to estimate the population proportion of Democrats who wear a mask to help prevent the spread of COVID-19 at 90% confidence with a margin of error no more than 1.28%. How many Democrats would they need to survey to do this? Use the data above as a preliminary sample.
\[n = \text{____}\]
#### Understanding Confidence Intervals:
Suppose you conduct a new survey this month and construct a 90% confidence interval for the population proportion of Americans who wear a mask to help prevent the spread of COVID-19 to be (0.883, 0.897). Which of the statements below is a correct interpretation of this confidence interval?
- **A.** There is a 90% chance that about 89% of Americans wear a mask to help prevent the spread of COVID-19.
- **B.** We can be 90% confident that the population proportion of Americans who wear a mask to help prevent the spread of COVID-19 is contained in the interval we constructed.
- **C.** If we collected another random sample of the same size, there is a 90% chance that the new sample proportion will be between 0.883 and 0.897.
- **D.** 90% of the time, the population proportion of Americans who wear a mask to help prevent the spread of COVID-19 is between 0.883 and 0.897.
### Detailed Graphical Explanation
There is no graph or diagram provided in the image above. However, understanding confidence intervals typically involves visualizing:
1. **The Sample Proportion:** This is the point estimate derived from your survey data.
2. **The Margin of Error:** This represents the range around the sample proportion that could likely contain the true population proportion.
3. **The Confidence Level:** This informs us about the probability (in percentage terms) that the confidence interval contains the true population proportion if we were to repeat the survey multiple times.
### Key Points to Note:
- **Sample Size Calculation:** To determine how many individuals Don Diego and Elena need to survey, use the formula for sample size in proportion estimation considering the desired margin of error and confidence level.
- **Correct Interpretation (Question 5):** The correct interpretation of a confidence interval is covered in statement **B**. This means we can
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