Data606 Presentation

Mael Illien
10/30/2019

Problem 7.13 Car insurance savings

A market researcher wants to evaluate car insurance savings at a competing company.

Based on past studies he is assuming that the standard deviation of savings is $100. He wants to collect data such that he can get a margin of error of no more than $10 at a 95% confidence level.

How large of a sample should he collect?

Problem parameters

  • The standard deviation of savings is $100
  • Margin of error of no more than $10
  • 95% confidence level
s <- 100
me <- 10
z <- qnorm(0.975)

Solve for n

\( ME = z^* \times \frac{s}{\sqrt{n}} \)
\( n = {\frac{z^* \times s}{ME}}^2 \)

n <- (z*s/me)^2
ceiling(n)
[1] 385

For a confidence level of 95% the minimum required sample size is 385.