Question

Suppose a 95% confidence interval for a population proportion is (0.27, 0.49). Rewrite this interval in the form of pˆ ± margin of error.​

Answer 1

Margin of error is equal to the radius of confidence interval or half of the width of confidence interval.

Margin of error = \frac{b-a}{2}

2

b−a

where (a,b) is the confidence interval.

Given confidence of interval is (0.27,0.49).

Margin of error = \frac{0.49-0.27}{2} = \frac{0.22}{2} = 0.11

2

0.49−0.27

=

2

0.22

=0.11

To write the given interval in terms of margin error, we have to find mid point of confidence interval = \frac{0.49+0.27}{2} = \frac{0.76}{2} = 038

2

0.49+0.27

=

2

0.76

=038

Now confidence interval=(mid point-margin of error, mid point+margin of error)

= (0.38-0.11, 0.38+0.11)

Hence confidence interval is 0.38±0.11