Recall Exercise 3.4.41 about the size of a sample needed for a margin of error of at most 0.03. What sample size is needed to have a margin of error of at most 0.03 for a 99% confidence interval? Use the same method as in Exercise 3.4.41 except use a multiplier of 2.576 that is used for 99% confidence.

Data from Exercises 3.4.41

You often see margins of errors in polling results listed as ±3%. What sample size do you need to have a margin of error of at most 0.03 for a 95% confidence interval? To answer this question, set the formula for the margin of error equal to 0.03 and solve for n. In other words, solve the equation 

for n given that the multiplier = 1.96 and p̂ = 0.50. (Having p̂ = 0.50 will give you the largest possible value for n so that whatever p̂ you have, the sample size will give an interval with a margin of error of at most 0.03.

Transcribed Image Text:

0.03 multiplier X √p(1-P)/n