Practice
- A university is interested in estimating the average daily commute time for its students. The population standard deviation is known to be 8 minutes. What sample size is needed to get a margin of error less than 3.0 for a 95% confidence interval?
Solution
From the problem we get the following information:
- A confidence interval of 95% has a critical value of \(z_c = 1.96\)
- The population standard deviation is \(\sigma=8\)
- The desired margin of error is \(E = 3.0\)
\[n = \left(\frac{z_c \sigma}{E}\right)^2 \left(\frac{1.96\cdot 8}{3}\right)^2 = 27.32\]
Rounding up, the required sample size is at least 28.
Return back to Lesson 18.4