Question

A poll taken this year asked 1009 adults whether they were fans of a particular sport and 55​% said they were. Last​ year, 56​% 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 90​% confidence in the estimate of the percentage of adults who are fans of the sport.

​b) If one wanted to be 85​% confident instead of 90​% confident, would the margin of error be larger or​ smaller?

​c) Find the margin of error for the poll taken this year if one wants 85​% confidence in the estimate of the percent of adults who are fans of the sport.

Answer 1

a)

Margin of error = Z$\alpha$/2 * sqrt (p( 1 - p) / n )

= 1.645 * sqrt ( 0.56 ( 1 - 0.56) / 1009)

= 0.0257

b)

Since critical z value at 0.15 significance is less than 0.10 significance level, the margin of error for 85% confidence

is smaller.

c)

Margin of error = Z$\alpha$/2 * sqrt (p( 1 - p) / n )

= 1.4395 * sqrt ( 0.56 ( 1 - 0.56) / 1009)

= 0.0225