A poll of 100 1 US adults split the sample into fou age groups ages 18-29. 3049
ID: 3317043 • Letter: A
Question
A poll of 100 1 US adults split the sample into fou age groups ages 18-29. 3049 5064 and 65+ In the youngest age group 65% said that theythought the US was ready for a woman president, as opposed to 32% who said no the country was not ready 396 were undeci e The samp e included 25 1 to 29-yearolds. a) Do you expect the 99% confidence interval for the true proportion of all 18-to 29-year olds who think the is ready for a woman president to be der ornar o e than the 99% confidence interval for the true proportion of all US adults? b) Construct a 99% confidence interval for the true proportion of all 18-to 29-year olds who believe the US is ready for a woman president. as wide as a) The 99% confidence interval for the true proportion of 18-to 29-year olds who think the US is ready for a woman president will be abou the 99% confidence interval for the true proportion of all US adults who think this. one-half equally one-fourth twice four times b) The 99% confidence interval is (L)%O%) (Round to one decimal place as needed.)Explanation / Answer
(a) Twice as wide
(b)
n = 250
p = 0.65
% = 99
Standard Error, SE = {p(1 - p)/n} = (0.65(1 - 0.65))/250 = 0.030166206
z- score = 2.575829304
Width of the confidence interval = z * SE = 2.57582930354892 * 0.0301662062579967 = 0.077703
Lower Limit of the confidence interval = P - width = 0.65 - 0.0777029980562486 = 0.572297
Upper Limit of the confidence interval = P + width = 0.65 + 0.0777029980562486 = 0.727703
The 99% confidence interval is [0.6, 0.7]