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home / study / math / statistics and probability / statistics and probability questions and answers / vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach ... Question: Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in or... Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent stdy, 82 patients with Type 2 diabetes underwent this procedure, and 59 of them experienced a recovery from diabetes. At the 0.01 significance level, test the claim that a majority of those with type 2 diabetes who undergo this surgery will recover from diabtes.

Explanation / Answer

alpha,a = 0.01
p0 = 0.5
x = 59 , n = 82 , p1=x/n = 0.72
.
H0: p = 0.5
H1: p > 0.5
.
standard error, SE = sqrt(p0(1-p0)/n)
SE = sqrt(0.5(1-0.5) / 82) = 0.05522
.
test statistic, z = (p1-p0) / SE
z = (0.72-0.5) / 0.05522) = 3.984
.
critical value = Za = Z0.01
critical value = 2.33
.
since z > critical value, hence reject H0
so we conclude that majority of those with type 2 diabetes who undergo this surgery will recover from diabtes..

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