A recent CNN poll found that in a random sample of 400 U.S. residents. 21% answered "Yes" to the question "Do you think life has ever existed o Mars?" Construct and interpret a 95% confidence interval for the proportion of all U.S. residents who believe life ever existed on Mars Assume a 95% confidence interval for the proportion is 0.125 to 0.384 (which it is not) Interpret the Confidence Interval We are confident that the interval from square to square captures the true v not at all square of square 95% 99% of US. residents think life ever existed on Mars?Explain 100% square

To construct a 95% confidence interval for the proportion of all U.S. residents who believe life ever existed on Mars, we need to use the sample proportion and the standard error of the proportion.<br /><br />Given information:<br />- Sample size (n) = 400 U.S. residents<br />- Sample proportion (p) = 21% = 0.21<br /><br />Step 1: Calculate the standard error of the proportion.<br />Standard error (SE) = √(p(1-p)/n)<br />SE = √(0.21(1-0.21)/400)<br />SE = √(0.21(0.79)/400)<br />SE = √(0.1659/400)<br />SE = √0.00041475<br />SE = 0.0203<br /><br />Step 2: Calculate the 95% confidence interval.<br />Margin of error (ME) = Z * SE<br />Where Z is the critical value for a 95% confidence level, which is approximately 1.96.<br />ME = 1.96 * 0.0203<br />ME = 0.0399<br /><br />Lower bound = p - ME = 0.21 - 0.0399 = 0.1701<br />Upper bound = p + ME = 0.21 + 0.0399 = 0.2499<br /><br />Therefore, the 95% confidence interval for the proportion of all U.S. residents who believe life ever existed on Mars is (0.1701, 0.2499).<br /><br />Interpretation:<br />We are 95% confident that the interval from 0.1701 to 0.2499 captures the true proportion of all U.S. residents who believe life ever existed on Mars.<br /><br />Regarding the statement "99% of U.S. residents think life ever existed on Mars," this is not accurate based on the given information. The 95% confidence interval suggests that we are 95% confident that the true proportion of U.S. residents who believe life ever existed on Mars is between 0.1701 and 0.2499, which is a range, not a specific percentage.