Question

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the 1229 males​ surveyed,185 responded that they had at least one tattoo. Of the

1030 females​ surveyed,138 responded that they had at least one tattoo. Construct a 95​% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.

Let

p 1 represent the proportion of males with tattoos and

p 2 represent the proportion of females with tattoos. Find the 95​% confidence interval for p1−p2.

Answer 1

	male		female
x1                =	185	x2                =	138
p̂1=x1/n1 =	185/1229 =0.1505	p̂2=x2/n2 =	138/1030=0.1340
n1                       =	1229	n2                       =	1030
estimated difference in proportion   =p̂1-p̂2   =0.1505-0.1340 =			0.0165
std error Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =sqrt(0.1505*(1-0.1505)/1229+0.1340*(1-0.1340)/1030)=			0.0147
for 95 % CI value of z=		1.960
margin of error E=z*std error =0.0147*1.96=		0.0289
lower bound=(p̂1-p̂2)-E=0.0165-0.0289 =		-0.0123
Upper bound=(p̂1-p̂2)+E=0.0165+0.0289=		0.0454
from above 95% confidence interval for difference in population proportion =(-0.0123 <p1-p2< 0.0454)

since confidence interval contains 0 within interval values we can not conclude that   proportion of males that have at least one tattoo differs significantly from the proportion of females