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 897 335 1232 Republicans 693 482 1175 Round all calculated values in this problem to 4 decimal places.
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 | 897 | 335 | 1232 |
| Republicans | 693 | 482 | 1175 |
Round all calculated values in this problem to 4 decimal places.
1. Provide a point estimate for the population proportion of Republicans who wore a mask to help prevent the spread of COVID-19 at the time of the survey.
2. Construct a 95% confidence interval for the population proportion of Republicans 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. There must be an expected count of at least 5 in every cell of the table.
D. The sample size must be at least 30 or the population data must be
4. Two STT200 students, Don Diego and Elena Montero, want to estimate the population proportion of Republicans who wear a mask to help prevent the spread of COVID-19 at 95% confidence with a margin of error no more than 1.25%. How many Republicans would they need to survey to do this? Use the data above as a preliminary sample. Round your ?∗z∗ value to EXACTLY 3 decimal places.
5. Suppose you conduct a new survey this month and construct a 95% 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?
B. If we collected another random sample of the same size, there is a 95% chance that the new sample proportion will be between 0.883 and 0.897.
C. We can be 95% 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.
D. There is a 95% chance that about 89% of Americans wear a mask to help prevent the spread of COVID-19.
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