Question

Use the following to answer questions 19-21 Breast cancer is one of the leading causes of death in women prior to age 50. A study of the effectiveness of regular breast self-examination (BSE) reported in the American Journal of Public Health found that 23 of 53 women who discovered a tumor through BSE had a tumor in an early stage. Of 178 women who discovered a tumor by accident, 48 had a tumor in an early stage. Let p1 and p2 denote the proportion of women who detected early stage tumor through BSE and by accident, and let p1 and p2 denote the corresponding estimates.

The SE of p1-p2 is:________

Answer 1

s e(
`p^(-) _(1) - p^(-) _(2)` ) = 0.07576

Explanation:

Step(i):-

The proportion of the first sample

`p^(-) _(1) = (x_(1) )/(n_(1) ) = (23)/(53) = 0.43396`

The proportion of the second sample

`p^(-) _(2) = (x_(2) )/(n_(2) ) = (48)/(178) = 0.2696`

Step(ii):-

Standard Error of (
`p^(-) _(1) - p^(-) _(2)`) is determined by

`se(p^(-) _(1) - p^(-) _(2)) = \sqrt{(p^(-) _(1) (1-p^(-) _(1) ))/(n_(1) )+(p^(-) _(2)(1-p^(-) _(2) ) )/(n_(2) ) }`

`se(p^(-) _(1) - p^(-) _(2)) = \sqrt{(0.43396) (1-0.43396 ))/(53 )+(0.2696(1-0.2696 ) )/(178) }`

on simplification, we get

s e(
`p^(-) _(1) - p^(-) _(2)` ) = 0.07576