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 12,887 university students and found that 8,014 of them support Bernie Sanders.

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

To calculate the required sample size, what value ofME. should we use in the formula below to calculate a 90% confidence interval within 8.84 percentage points? Give your answer to 4 decimal places.

n=p*(1−p*)(z*ME)2

Answer 1

Solution :

Given that,

n = 12887

x = 8014

Point estimate = sample proportion = = x / n = 8014 / 12887 = 0.6219

1 - = 1 - 0.6219 = 0.3781

margin of error = E = 0.0884

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05  = 1.645

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.0884)2 * 0.6219 * 0.3781

= 81.42

sample size = n = 82