Question

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the 1209 males​ surveyed, 185 responded that they had at least one tattoo. Of the 1009 females​ surveyed, 129 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.

Answer 1

Here, , n1 = 1209 , n2 = 1009
p1cap = 0.153 , p2cap = 0.1278

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.153 * (1-0.153)/1209 + 0.1278*(1-0.1278)/1009)
SE = 0.0148

For 0.95 CI, z-value = 1.96
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.153 - 0.1278 - 1.96*0.0148, 0.153 - 0.1278 + 1.96*0.0148)
CI = (-0.0038 , 0.0542)

There is no evidence that the proportions are significantly different