Question

2020 Election ~ Bernie Sanders is a popular presidential candidate among university students for the 2020 presidential election. Leading into Michigan’s presidential primary election in 2020, a journalist, Lauren took a random sample of 11,663 university students and found that 8,891 of them support Bernie Sanders.

Using this data, Lauren wants to estimate the actual proportion of university students who support Bernie Sanders.

What is the required sample size to calculate a 95% confidence interval within 3.05 percentage points? Use z*=1.96.z*=1.96.

n=p*(1−p*)(z*ME)2

Answer 1

The sample size formula is given as below:

n = p*q*(Z/E)^2

We are given

p = 8891/11663 = 0.762325

q = 1 – p = 0.237675

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Margin of error = E = 0.0305

The sample size is given as below:

n = p*q*(Z/E)^2

n = 0.762325*0.237675*(1.96/0.0305)^2

n = 748.2317

Required sample size = 749