Question

A poll taken this year asked 1034 adults whether they were fans of a particular sport and 42​% said they were. Last​ year, 41​%

of a​ similar-size sample had reported being fans of the sport. Complete parts a through e below.

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.

​d) Find the margin of error for the poll taken this year if one wants 95​% confidence in the estimate of the percent of adults who are fans of the sport.

Answer 1

Answer)

N = 1034

A)

P = 0.42 (42%)

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 434.28

N*(1-p) = 599.72

Both the conditions are met so we can use standard normal z table to estimate the margin of error (MOE)

MOE = Z*Standard error

Standard error = √{p*(1-p)}/√n

Critical value z from z table for 90% confidence level is 1.645

P = 0.42

Margin of error = 1.645*√{0.42*(1-0.42)}/√1034

MOE = 0.02524900538

B)

For 95%

Z = 1.96 (from z table)

Rest is same

MOE = 0.03008392130