Question

In a recent poll, 250 people were asked if they liked dogs, and 47% said they did. Find the margin of error of this poll, at the 90% confidence level.

Give your answer to three decimals

Answer 1

Solution :

Given that,

n = 250

Point estimate = sample proportion = = 0.47

1 -   = 1-0.47 =0.53

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.47*0.53) / 250)

E = 0.052

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.47-0.052 < p < 0.47+0.052

0.418< p < 0.522