A poll taken this year asked 1041 adults whether they were fans of a particular
ID: 3222906 • Letter: A
Question
A poll taken this year asked 1041 adults whether they were fans of a particular sport and 33% said they were. Last year, 32% of a similar-size sample had reported being fans of the sport.
a) Find the margin of error for the poll taken this year if one wants 95% confidence in the estimate of the percentage of adults who are fans of the sport
b) Explain what the margin of error means.
c) If one wanted to be 99% confident instead of 95%, would the margin of error be larger or smaller?
d) Find the margin of error for the poll taken this year if one wants 99% confidence i nthe estimate of the percent of adults who are fans of the sport.
Explanation / Answer
here std error =(p(1-p)/n)1/2 p=0.33 and n=1041
=0.0146
for 95% CI, z=1.96
hence margin of error =z*std error =0.0286 ~2.86%
b)this is possible error in the estimated statistic for a parameter at given confidence interval
c)iot would be larger as value of z increases with increased confidence interval
d)for 99% CI, z=2.5758
hence margin of error =0.0375 ~3.75%