Question

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the 1210 males​ surveyed,184 responded that they had at least one tattoo. Of the 1039

females​ surveyed,138 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

p 1 minus p 2p1−p2.

The lower bound is

The upper bound is

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

Answer 1

given : For male : n1=1210 , X1=184

For female : n2=1039 , X2=138

The sample proportions are given by ,

The pooled estimate is ,

Now , ; From standard normal distribution table

Therefore , the 90% confidence interval for p1-p2 is ,

The lower bound is -0.0050

The upper bound is 0.0436