Question

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the 1216 males​ surveyed, 179 responded that they had at least one tattoo. Of the 1030 females​ surveyed, 139 responded that they had at least one tattoo. Construct a 99​% 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 99​% confidence interval for p1−p2.

WHAT IS THE LOWER AND UPPER BOUND?

Answer 1

Solution :

Given that,

₁ = x₁ / n₁ = 0.147

₂ = x₂ / n₂ = 0.135

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.147 - 0.135

= 0.012

2)

Our aim is to construct 99% confidence interval.

= 1.96 (use z table)

Margin of error =   *

=

= 0.038

3) Required interval is

Point estimate   Margin of error

0.012   0.038

(0.012 - 0.038 , 0.012 +  0.038 )

(-0.026, 0.050)

Lower bound = -0.026

Upper bound = 0.050