Question

How effective is gastric bypass surgery in maintaining weight loss in extremely obese people? A Utah-based study conducted between 2000 and 2011 found that 76% of 418 subjects who had received gastric bypass surgery maintained at least a 20% weight loss six years after surgery.

Give a 90% confidence interval for the proportion of those receiving gastric bypass surgery that maintained at least a 20% weight loss six years after surgery. Interpret your interval in the context of the problem.

Answer 1

We need to construct the 90% confidence interval for the population proportion. We have been provided with the following information about the sample proportion:

Sample Proportion =	0.76
N =	418

The critical value for α=0.1 is z_c = 1.645. The corresponding confidence interval is computed as shown below:

We are 90% confident that the proportion of those receiving gastric bypass surgery that maintained at least a 20% weight loss six years after surgery will lie in the interval (0.726, 0.794)