Cigarette Costs? In an American Express survey of 1000 adults 18 and older, 62% said that cigarettes should cost more to help offset potential negative health effects. Use the sample data to construct a 95% confidence interval estimate of the percentage of all adults who share that same belief. What can we conclude about a claim that half of all adults share that same belief?

Solution 2CRE Step1: From the above given problem we have, X ~B(p, q) N = 1000 p = 62% = 0.62 q = (1-p) = 1-0.62 = 0.38 Now, 95% confident interval can be calculated by using the formula X ± Z 2* SE ……..(1) Where, X = mean = p = 0.62 pq And SE = n (0.62)(0.38) = 1000 = 0.015 To find the critical value, a/2 : Here, the confidence level is 95%. Convert the percentage to a decimal, .95, and divide it by 2 to get .475. Then, check out the z table to find the corresponding value that goes with .475. You'll see that the closest value is 1.96, at the intersection of row 1.9 and the column of .06. Therefore Z 2 value is 1.96 Now, 95% confident interval is = 0.62 ±1.96 * 0.015 = 0.62 ± 0.0294 = (0.5906, 0.6494) 59% < p < 65% This interval does not contain half of the sample, hence claim should be rejected.