Gastric bypass surgery How effective is gastric bypass surge

Gastric bypass surgery. 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.²²

(a)Are the conditions for the use of the large-sample confidence interval met?Explain.

(b)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.

(c)Interpret your interval in the context of the problem.

Solution

a)
Yes, it is met, since the sample
size is above >30
b)
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=317.68
Sample Size(n)=418
Sample proportion = x/n =0.76
Confidence Interval = [ 0.76 ±Z a/2 ( Sqrt ( 0.76*0.24) /418)]
= [ 0.76 - 1.64* Sqrt(0.0004) , 0.76 + 1.64* Sqrt(0.0004) ]
= [ 0.7257,0.7943]

c)
We are 90% confident the meav proportion rate of people who maintained at least a
20% weight loss six years after surgery is lies is 75.27% to 70.43%