Introduction to Estimation & Confidence Intervals for a Proportion

Question 1

How large does n need to be for the CLT to apply for proportions?

Answer 1

If we are dealing with a proportion, we would usually want n > 50, preferably larger than 100 before we rely on the Central Limit Theorem to tell us that p̂ (sample proportion, x/n) is normally distributed

Question 2

What does the CLT tell us about proportions?

Answer 2

• X/n = p̂~N(p, p(1-p)/n)
  
  • p̂ = estimated form data
  • p = true population proportion, probabilty
  • p(1-p)/n = spread
• The sample proportion has a normal disitubiton, with a centre at p, the population proportion, and variance of p(1-p)/n

Question 3

What is the standard error of the sample proportion?

Answer 3

√(p(1-p)/n)