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 11,834 university students and found that 8,211 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 of Z* should we use in the formula below to calculate a 90% confidence interval within 4.62 percentage points? Give your answer to 4 decimal places.

n= p* (1-p*) (z*/ME)^2

Answer 1

Solution :

Given that,

n = 11834

x = 8211

Point estimate = sample proportion = = x / n = 8211 / 11834 = 0.6938

1 - = 1 - 0.6938 = 0.3062

margin of error = E = 0.0462

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

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

= (1.96 / 0.0462 )2 * 0.6938 * 0.3062

= 382.35

sample size = n = 383