Question

Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. From research on other college​ campuses, you believe the proportion will be near 25​%.

What sample size is needed if you wish to be 90​% confident that your estimate is within 0.02 of the true​ proportion?

Answer 1

The following information is provided,
Significance Level, α = 0.1, Margin of Error, E = 0.02

The provided estimate of proportion p is, p = 0.25
The critical value for significance level, α = 0.1 is 1.645.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.25*(1 - 0.25)*(1.645/0.02)^2
n = 1268.45

Therefore, the sample size needed to satisfy the condition n >= 1268.45 and it must be an integer number, we conclude that the minimum required sample size is n = 1269

Ans : Sample size, n = 1269