I need help with all of them plz. ### Statistical Analysis: Estimating Population Proportion and Confidence Intervals#### 4. Estimating Population ProportionTwo STT200 students, Don Diego and Elena Montero, aim to estimate the population proportion of Democrats who wear a mask to help prevent the spread of COVID-19 at a 90% confidence level with a margin of error no more than 1.28%. To achieve this, they need to determine the necessary sample size. Let's denote the sample size as \( n \).\[ n = \]#### 5. Understanding Confidence IntervalsConsider a new survey conducted this month, which constructs a 90% confidence interval for the population proportion of Americans who wear a mask to help prevent the spread of COVID-19. The interval is given as (0.883, 0.897). To understand this interval, let's evaluate which statement accurately interprets it:1. **A.** There is a 90% chance that about 89% of Americans wear a mask to help prevent the spread of COVID-19.2. **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.3. **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 0.897.4. **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.### Explanation of Choices in Question 5:- **Choice A** is incorrect because the confidence interval specifies a range (0.883 to 0.897), not a specific proportion. - **Choice B** is correct. A 90% confidence interval means we can be 90% confident that the true population proportion lies within the interval (0.883, 0.897).- **Choice C** is incorrect because the confidence interval applies to the population parameter, not to new samples. Each new sample would produce its own interval. - **Choice D** is incorrect because it misinterprets the idea of confidence intervals; it suggests the interval will encompass the true proportion 90% of the time, rather than expressing confidence about the interval containing the true proportion.Understanding these ### Understanding Mask Usage During COVID-19: A Survey AnalysisIn light of evidence about how COVID-19 spreads, the CDC recommends that people wear a cloth facemask to cover their nose and mouth in community settings. 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:#### Mask Usage by Political Affiliation| | Masked | Unmasked | Total ||---------------|--------|----------|-------|| Democrats | 829 | 309 | 1138 || Republicans | 640 | 445 | 1085 |**Note:** Round all calculated values in this problem to 4 decimal places.1. **Provide a point estimate for the population proportion of Democrats who wore a mask to help prevent the spread of COVID-19 at the time of the survey.** \(\hat{p} = \_\_\_\_\_\_\_\_\_\_\_\_\_\)2. **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.** (\_\_\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_\_\_)3. **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.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

Note: Since you have posted a question with multiple subparts, we will solve the first three…

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 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: Masked Unmasked Total Democrats 829 309 1138 Republicans 640 445 1085 Round all calculated values in this problem to 4 decimal places. 1. Provide a point estimate for the population proportion of Democrats who wore mask to help prevent the spread of COVID-19 at the time of the survey. 2. Construct a 90% confidence interval for the population proportion of Democrats who wore time of the survey. mask to help prevent the spread of COVID-19 at the 3. Which of the following conditions must be met for the confidence interval to be valid? Select all that apply. OA. The observations must be independent of one another. OB. There must be at least 10 'success' and 10 'failure' observations. OC. The sample size must be at least 30 or the population data must be normally distributed. OD. There must be an expected count of at least 5 in every cell of the table.

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P