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 more higher.Suppose a current survey of 1000 random Canadians found that 245 were obese.Create a 95% confidence interval for the proportion of Canadians that are currently obese.
A)Based on the data,we are 95% confident the current proportion of obese Canadians is between 22% and 24%.
B)Based on the data,we are 95% confident the current proportion of obese Canadians is between 17.97% and 26.03%.
C)Based on the data,we are 95% confident the current proportion of obese Canadians is between 17.97% and 27.03%.
D)Based on the data,we are 95% confident the current proportion of obese Canadians is between 21.8% and 27.2%.
E)Based on the data,we are 95% confident the current proportion of obese Canadians is between 22.44% and 26.56%.

Question

Quizplus · Accepted Answer

To create a 95% confidence interval, we can use the formula:

sample proportion ± z-score x standard error

where the sample proportion is the proportion of obese Canadians in the sample (245/1000 = 0.245), the z-score corresponds to the level of confidence (1.96 for 95% confidence), and the standard error is calculated as:

sqrt[(sample proportion x (1 - sample proportion)) / sample size]
= sqrt[(0.245 x 0.755) / 1000]
= 0.015

Plugging in these values, we get:

0.245 ± 1.96 x 0.015
= 0.245 ± 0.0294

Therefore, the 95% confidence interval is (0.2156, 0.2744), or approximately 21.6% to 27.4%. The closest answer choice is D, which gives a range of 21.8% to 27.2%.