Question

A study at Harvard found that 44% of their students binge drink. You are at Princeton doing a similar study. How many people do you need to interview to get your interval width down to 10 percentage points? For a 95% CI, what is that sample size?

Answer 1

Solution:

Given that,

= 0.44

1 - = 1 - 0.44 = 0.56

margin of error = E =10% = 0.10 / 2 = 0.05

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Sample size = n = ((Z _{/ 2}) / E)² * * (1 - )

= (1.960 / 0.05 )² * 0.44 * 0.56

= 378.628

= 379

n = sample size = 379