Question

A Gallup poll asked 175 American adults whether they were baseball fans and 65% said they were. Find the margin of error if we want to create a 90% confidence interval for the true proportion of American adults who are baseball fans. Write your answer in decimal format to 3 decimal places. For example, 0.123 would be the correct format.

Answer 1

Solution :

Given that,

n = 175

Point estimate = sample proportion = =65%=0.65

1 - = 1-0.65=0.35

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645} ( Using z table )

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

= 1.645 (((0.65*0.35) / 175)

= 0.059

Margin of error = E=0.059