Question

According to the National Institutes of Health (NIH), a person is obese if his or her body mass index (BMI) is 30 or above. In a simple random sample of 800 college-age adults (18-24), 96 of the subjects were found to be obese. Find a 95% confidence interval for the proportion of all college-age adults who are obese. Write a summary sentence for the confidence interval you calculated

		(0.090, 0.150)
		(0.097, 0.143)
		(0.109, 0.131)
		(0.119, 0.121)

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 96 / 800 = 0.120

1 - = 1 - 0.120 = 0.88

Z/2 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * (((0.120 * 0.88) / 800)

Margin of error = E = 0.023

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.120 - 0.023 < p < 0.120 + 0.023

0.097 < p < 0.143

The 95% confidence interval for the population proportion p is : (0.097 , 0.143)