Question

How effective is gastric bypass surgery in maintaining weight loss in extremely obese people? A study conducted found that 71% of an SRS of 437 subjects who had received gastric bypass surgery maintained at least a 20% weight loss six years after surgery.

1) 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. (Round your answers to four decimal places.)

Answer: _____ to _____

2) Interpret your interval in the context of the problem. (Round your answers to two decimal places.)

Answer: Based on this study, we estimate with 90% confidence that between _____ % and _____ % of all gastric bypass patients will maintain at least a 20% weight loss for six years after surgery.

Answer 1

Solution :

Given that,

1) n = 437

Point estimate = sample proportion = = 0.71

1 - = 1 - 0.71 = 0.29

At 90% confidence level

= 1 - 90%

=1 - 0.90 = 0.10

/2 = 0.05

Z/2 = Z0.05  = 1.645

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

= 1.645 (((0.71 * 0.29) / 437)

= 0.0357

A 90% confidence interval for population proportion p is ,

± E   

= 0.71  ± 0.0357

= ( 0.6743, 0.7457 )

2) We estimate with 90% confidence that between 67.43% and 74.57% of all gastric bypass patients will maintain at least a 20% weight loss for six years after surgery.