Question

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the 1229 males​ surveyed, 182 responded that they had at least one tattoo. Of the 1020 females​ surveyed, 137 responded that they had at least one tattoo. Construct a 90​% 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 p1 represent the proportion of males with tattoos and p2 represent the proportion of females with tattoos. Find the 90​% confidence interval for p1−p2. The lower bound is --.

The upper bound is --.

​(Round to three decimal places as​ needed.)

Answer 1

Here, , n1 = 1229 , n2 = 1020
p1cap = 182/1229 = 0.1481 , p2cap = 137/1020 = 0.1343

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.1481 * (1-0.1481)/1229 + 0.1343*(1-0.1343)/1020)
SE = 0.0147

For 90% CI, z-value = 1.64

Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.1481 - 0.1343 - 1.64*0.0147, 0.1481 - 0.1343 + 1.64*0.0147)
CI = (-0.01 , 0.038)
lower bound : -0.010

upper bound: 0.038