A sample survey finds that 72 percent of a sample of 1,017 adults in Kentucky wanted the recently elected governor to retain the health-insurance plan mandated by the Affordable Care Act. If that sample were a simple random sample from the population of all Ohio adults, what would be the 99 percent confidence interval for the percent of all Kentucky adults who feel that way?
A) 66 to 74 percent
B) 67 to 75 percent
C) 68 to 76 percent
D) 67 to 77 percent
E) 66 to 78 percent

Question

Quizplus · Accepted Answer

To find the 99% confidence interval for the proportion of all Kentucky adults who want to retain the health-insurance plan mandated by the Affordable Care Act, we can use the formula:

CI = p ± z*√(p(1-p)/n)

where p is the sample proportion (0.72), z is the z-score corresponding to a 99% confidence level (2.576), and n is the sample size (1017).

Plugging in the values, we get:

CI = 0.72 ± 2.576*√(0.72*0.28/1017)
CI = 0.72 ± 0.032
CI = (0.688, 0.752)

Thus, the 99% confidence interval for the proportion of all Kentucky adults who want to retain the health-insurance plan mandated by the Affordable Care Act is 68.8% to 75.2%.

The best choice for the answer is C, which gives the correct confidence interval.

A Sample Survey Finds That 72 Percent of a Sample