Question

A polling company conducts an annual poll of adults about political opinions. The survey asked a random sample of 314 adults whether they think things in the country are going in the right direction or in the wrong direction. 51% said that things were going in the wrong direction. How many people would need to be surveyed for a 90% confidence interval (z*=1.645) to ensure the margin of error would be less than 3%? Round your answer to the appropriate integer.

Answer 1

The following information is provided,
Significance Level, α = 0.1, Margin of Error, E = 0.03

The provided estimate of proportion p is, p = 0.51
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 = 0.51*(1 - 0.51)*(1.645/0.03)^2
n = 751.37

sample size = 751 (if rounded to nearest whole number)
= 752 (if rounded to next integer)