Question

On the Allien wolrd of Bloorn, a simple radom sample of 35 Bloorians was taken, and 20 of them preferred the Ablex political party. Construct a 95% confidence interval for the proportion of Bloornians who prefere the Ablex party

Answer 1

Solution :

Given that,

n = 35

x = 20

Point estimate = sample proportion = = x / n = 20 / 35 = 0.571

1 - = 1 - 0.571 = 0.429

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.960}

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

= 1.96 (((0.571 * 0.429) / 35)

= 0.164

A 95% confidence interval for population proportion p is ,

± E

= 0.571 ± 0.164

= ( 0.407, 0.735 )