Question

Confidence Levels: Given specific sample data (for example poll results from 1000 people of whom 14% indicated their favorite pie was chocolate) which confidence interval is wider: the 95% confidence interval or the 80% confidence interval? Why is it wider?  

Where can I find the correct formula to answer this question?

Answer 1

Solution :

Given that,

n = 1000

Point estimate = sample proportion = = 014

1 - = 1 - 0.14 = 0.86

a) At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.14 * 0.86) / 1000)

= 0.022

A 95% confidence interval for population proportion is ,

   - E < < + E

0.14 - 0.022 < < 0.14 + 0.022

( 0.118 < < 0.162 )

b) At 80% confidence level

= 1 - 80%

=1 - 0.80 =0.20

/2 = 0.10

Z/2 = Z0.10 = 1.282

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.282 (((0.14 * 0.86) / 1000)

= 0.014

A 80% confidence interval for population proportion is ,

   - E < < + E

0.14 - 0.014 < < 0.14 + 0.014

( 0.126 < < 0.154 )

The 95% confidence interval is wider