(a) 25% of the surveyed adults, or 87.5 individuals, admitted to driving intoxicated.
(b) We're 95% confident the true proportion of intoxicated drivers is between 20% and 25%.
(c) The maximum error for this confidence interval is 4.6%.
(d) To achieve 99% confidence with a 5% margin of error, you need at least 534 adult drivers surveyed.
(a) To find the number of adults who admitted to driving intoxicated, simply multiply the percentage by the total sample size: 25% (0.25) * 350 adults = 87.5 adults.
(b) The 95% confidence interval tells us the range within which the true proportion of intoxicated drivers in the whole population likely falls, with 95% certainty. To calculate it, we use statistical formulas, but in summary, the interval is roughly 0.20 (20%) on the lower end and 0.25 (25%) on the upper end.
(c) The margin of error is the maximum distance from the sample proportion (25%) to the edge of the confidence interval. In this case, it's the difference between the estimated proportion and the lower or upper bound, whichever is larger: 0.25 - 0.20 = 0.046, or 4.6%.
(d) For higher confidence and lower error, you need a larger sample size. Using statistical calculations, we find that to achieve 99% confidence with a 5% margin of error, you would need at least 534 adults surveyed in your sample.
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