Question

A recent survey on marriage trends reported that 4% of the respondents said single women having children is a "good thing". The 95% confidence interval is from 2.9% to 5.1%. (n= 1229)

(a) What is the Margin of Error

(b) What does "95% confidence" mean?

(c) If we wanted a 99& confidence interval, would the interval be wider or smaller than 2.9% to 5.1%

Answer 1

1. Let sample proportion be phat.

Lower CI = phat - E = 0.029…… (1)

Upper CI = phat + E = 0.051……. (2)

Subtracting (2) from (1)

2*E = (0.051 – 0.029) = 0.022

E = 0.011

The margin of error is 0.011.

2. The 95% confidence means that 95% of all possible samples of 1229 people have a 95% confidence interval that contain the population proportion p.
3. If we wanted a 99% confidence interval then the interval would be wider than 2.9% to 5.1%.

This indicate that we have more reliable region. But it is less precise.