Question

To conduct a research project on whether college students purchase textbooks, the number of students to sampled needs to be calculated.
To estimate the population proportion, we decide to use a 95% level of confidence. The desired margin of error is to be within +/- 10%. There is no prior estimate of the population proportion.
What sample size would you recommend?
Express your solution rounded in the appropriate way.

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 10%=0.10

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 = 1.96

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.96/ 0.10)² * 0.5 * 0.5

= 96.04

Sample size = 96

(when p^ is not given assume p^=0.5)