Question

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the 1206 males​ surveyed, 198 responded that they had at least one tattoo. Of the 1046 females​ surveyed, 127

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 1p1 represent the proportion of males with tattoos and p 2p2

represent the proportion of females with tattoos. Find the 95​% confidence interval for p 1 minus p 2p1−p2.

Answer 1

We are 95% confident that true difference in the proportion of males that have at least one tattoo and the proportion of females that have at least one tattoo lie in the interval (0.0140, 0.0716) or (1.4%, 7.16%). Since confidence interval does not contain zero so difference between the proportions is significant.