You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 78%. You would like to be 95% confident that your estimate is within 1% of the true population proportion. How large of a sample size is required?

Introduction:

The confidence interval for the population proportion, p at the 100 (1 – α) % confidence level is:

Here, n is the sample size, p is the sample proportion, and z_α/2 is the upper critical value of the standard normal distribution.

The margin of error in this confidence interval is:

When population proportion, p is known, p̂ will be substituted by the population proportion, p in the expression for E.