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

Question

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

Answer 1

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.Given information:- Sample size (n) = 400 U.S. residents- Sample proportion (p) = 21% = 0.21Step 1: Calculate the standard error of the proportion.Standard error (SE) = √(p(1-p)/n)SE = √(0.21(1-0.21)/400)SE = √(0.21(0.79)/400)SE = √(0.1659/400)SE = √0.00041475SE = 0.0203Step 2: Calculate the 95% confidence interval.Margin of error (ME) = Z * SEWhere Z is the critical value for a 95% confidence level, which is approximately 1.96.ME = 1.96 * 0.0203ME = 0.0399Lower bound = p - ME = 0.21 - 0.0399 = 0.1701Upper bound = p + ME = 0.21 + 0.0399 = 0.2499Therefore, the 95% confidence interval for the proportion of all U.S. residents who believe life ever existed on Mars is (0.1701, 0.2499).Interpretation: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.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.

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