Sample proportion is 070 Two researchers study the same subj

Sample proportion is 0.70. Two researchers study the same subjects and obtain two different half-widths: (0.632, 0.768) and (0.652, 0.788). Which one is wrong and why?

Solution

The second researcher is wrong, because sample proportion should be the mid-point of the half-width.

Mid point of half width for :

1st researcher: (0.632+0.768)/2 = 0.7

2nd researcher: (0.652+0.788)/2 = 0.72

Thus, 2nd researcher is wrong.