Question

A survey​ asked, "Do you currently have tattoos on your​ body?" Of the 1239 males​ surveyed, 179 responded that they had at least one tattoo. Of the 1057 females​ surveyed, 141 responded that they had at least one tattoo. Test if the male population proportion is greater in having tattoos at a 95​% confidence level.

What is the test statistics?

What is the critical value?

Answer 1

H0: p1 = p2

Ha: p1 > p2

Sample proportion 1= 179 / 1239 = 0.1445

Sample proportion 2 =141 / 1057 = 0.1334

Test statistics

z = (1 - 2) / sqrt[ 1 ( 1 - 1 ) / n1 + 2 ( 1 - 2 ) / n2 ) ]

= ( 0.1445 - 0.1334) / sqrt( 0.1445 * 0.8555 / 1239 + 0.1334 * 0.8666 / 1057)

= 0.77

This is test statistics value.

Critical value at 0.05 level = 1.645