Question

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the

12271227

males​ surveyed,

190190

responded that they had at least one tattoo. Of the

10601060

females​ surveyed,

129129

responded that they had at least one tattoo. Construct a

9999​%

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 1p1

represent the proportion of males with tattoos and

p 2p2

represent the proportion of females with tattoos. Find the

9999​%

confidence interval for

p 1 minus p 2p1−p2.

The lower bound is

nothing.

The upper bound is

nothing.

Answer 1

Here, , n1 = 1227 , n2 = 1060
p1cap = 0.1548 , p2cap = 0.1217

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.1548 * (1-0.1548)/1227 + 0.1217*(1-0.1217)/1060)
SE = 0.0144

For 0.99 CI, z-value = 2.58
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.1548 - 0.1217 - 2.58*0.0144, 0.1548 - 0.1217 + 2.58*0.0144)
CI = (-0.0041 , 0.0703)

Lower bound = -0.0041

upper bound = 0.0703