According to the 2004 Canadian Community Health Survey,23.1% of Canadians aged 18 or older were considered obese; that is,they had a body mass index (BMI)of 30 or higher.Suppose a current survey in 2014 of 1000 random Canadians found that 245 were obese.Create a 95% confidence interval for the proportion of Canadians that are currently obese.

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval for a proportion:

CI = p ± z*sqrt((p*(1-p))/n)

where p is the sample proportion, z is the z-score corresponding to the desired level of confidence (1.96 for 95% confidence), and n is the sample size.

Plugging in the values given:

p = 245/1000 = 0.245

z = 1.96

n = 1000

CI = 0.245 ± 1.96*sqrt((0.245*(1-0.245))/1000)

CI = 0.245 ± 0.025

CI = (0.22, 0.27)

Therefore, we can say, with 95% confidence, that the true proportion of obese Canadians is between 21.8% and 27.2%. The best choice is D.