Gastric bypass surgery . How effective is gastric bypass surgery in maintaining
ID: 3355878 • Letter: G
Question
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.
Explanation / Answer
PART A.
Points to pass for normal approximation:
1) experiment consistes of a sequence of n identical trials
2) only 2 outcomes are possible on each trail, success or failure
3) trials are independent & below conditions should satisfy
n*p>5, 418*0.76> 5 => 317.68>5
n*(1-p)>5, 418*0.24> 5 => 100.32>5
can use normal approximation
and conditions for the use of the large-sample confidence interval met
PART B.
TRADITIONAL METHOD
given that,
sample size(n)=418
success rate ( p )= x/n = 0.76
I.
sample proportion = 0.76
standard error = Sqrt ( (0.76*0.24) /418) )
= 0.0209
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.645
margin of error = 1.645 * 0.0209
= 0.0344
III.
CI = [ p ± margin of error ]
confidence interval = [0.76 ± 0.0344]
= [ 0.7256 , 0.7944]
c.
interpretations:
1. We are 90% sure that the interval [ 0.7256 , 0.7944] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population proportion
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