MY NOTES An article about financial literacy in America summarized a national survey of 2,000 U.S. adults over the age of 18. The sample was selected to be representative of adults in this age group. I USE SALT (a) of those surveyed, 64% reported that they had credit card debt. Use this information to construct a 95% confidence interval for the proportion of all adults in this age group who have credit card debt. (Enter your answer using interval notation. Round your numerical values to three decimal places.) Interpret the interval. We are 95% confident that the true proportion of all adults in the United States who have credit card debt is directly in the middle of this confidence interval. We are 95% confident that the true proportion of all adults in the United States who have credit card debt is within this confidence interval. There is a 95% chance that the mean number of all adults in the United States who have credit card debt is directly in the middle of this confidence interval. There is a 95% chance that the true proportion of all adults in the United States who have credit card debt is directly in the middle of this confidence interval. We are 95% confident that the mean number of all adults in the United States who have credit card debt is within this confidence interval. (b) Of those surveyed, 25% reported that they always pay their bills on time. Use this information to construct a 90% confidence interval for the proportion of all adults in this age group who always pay their bills on time. (Enter your answer using interval notation. Round your numerical values to three decimal places.) Interpret the interval. There is a 90% chance that the mean number of all adults in the United States who always pay their bills on time is directly in the middle of this confidence interval. We are 90% confident that the mean number of all adults in the United States who always pay their bills on time is within this confidence interval. We are 90% confident that the true proportion of all adults in the United States who always pay their bills on time is directly in the middle of this confidence interval. We are 90% confident that the true proportion of all adults in the United States who always pay their bills on time is within this confidence interval. There is a 90% chance that the true proportion of all adults in the United States who always pay their bills on time is directly in the middle of this confidence interval. (c) Give two reasons why the confidence interval from part (b) is narrower than the confidence interval from part (a). The confidence interval in part (b) is narrower because of 0.25 is farther from 0.5 than of 0.64. Another reason is that the confidence level in part (b) is smaller than in part (a).