America's image abroad ~ Around the world, favorable views of the U.S. rebounded in 2021, according to an article published by the Pew Research Center in June 2021. Between March 12 and May 26, 2021, Pew Research contacted a nationally representative sample of adults in 16 different countries around the world. One of the questions in the survey asked participants whether they have a favorable view of the U.S.Of the 1002 respondents who participated in the survey in South Korea, 771 said that their view of the U.S. is favorable. (Values given in this problem are consistent with the results reported in the article.)Assume the respondents are a simple random sample of all adults in South Korea. Round all calculated answers to 4 decimal places unless otherwise indicated.1. Using the information given above, construct a 90% confidence interval for the true proportion of adults in South Korea who have a favorable view of the U.S.( , )

2. Which of the following conditions must be met for the confidence interval to be valid? Select all that apply. A. There must be at least 10 'success' and 10 'failure' observations in the sample. B. The sample proportion must be normally distributed. C. The value for p must be less than 0.10 to provide evidence against the null hypothesis. D. The observations must be independent of one another.

3. The information from the sample described above estimates the standard error to be SEp^=SEp^= 0.0133. Which of the statements below is a correct interpretation of this standard error?A. The sample proportion is different from the true proportion of adults in South Korea with a favorable view of the U.S. approximately 1.33% of the time. B. There is a 1.33% chance that the sample proportion is contained within any confidence interval for the true proportion of adults in South Korea with a favorable view of the U.S. C. On average, for repeated simple random samples of this size, we expect the sample proportion to be approximately 0.0133 from the true population proportion of adults in South Korea with a favorable view of the U.S. D. We have strong evidence that the true proportion of adults in South Korea with a favorable view of the U.S. is contained in the confidence interval constructed with this sample information.

4. Pew Research also surveyed a random sample of 1124 adults living in Singapore. Using the sample information reported in the article, we calculate a 95% confidence interval for the true proportion of adults in Singapore with a favorable view of the U.S. to be (0.481, 0.618).Which of the following statements are appropriate interpretations in this scenario? Select all that apply. A. If the researchers collected 100 samples of size n = 1124 from this population and constructed a 95% confidence interval for each of the 100 samples, they could expect approximately 95 of them to contain the true proportion of adults in Singapore with a favorable view of the U.S. B. On average, 95% of the time we can expect any sample proportion from a sample of 1124 adults in Singapore with a favorable view of the U.S. to be in the interval (0.481, 0.618). C. We can be 95% confident that the true proportion of adults in Singapore with a favorable view of the U.S. is contained in the interval (0.481, 0.618). D. We can be 95% confident that, on average, the margin of error will vary no more than the size of the standard error.

5. If, instead, we used the results for Singapore to calculate a 99% confidence interval for the true proportion of adults in Singapore with a favorable view of the U.S., this new interval would be ? wider than narrower than the same width as the 95% confidence interval.6. For this article, Pew Research surveyed adults in 16 different countries. Overall, 61% of survey respondents said their view of the U.S. was favorable. Bulgaria was not one of the these 16 countries. If a research group in Bulgaria wanted to construct a 90% confidence interval for the proportion of adults in that country who have a favorable view of the U.S. with a margin of error of no more than 2.5%, what size sample should they take?Use the overall value from the Pew Research survey as a planning value for pp, that is, p=0.61p=0.61. Round your zz value to exactly 3 decimal places. Your answer should be an integer.n=n=