Practice
- A manufacturer claims that its LED light bulbs have an average lifespan of 1,200 hours. A consumer protection agency wants to verify this claim. The population standard deviation is known to be 100 hours. What sample size is needed to get a margin of error less than 35 for a 99% confidence interval?
Solution
From the problem we get the following information:
- A confidence interval of 99% has a critical value of \(z_c = 2.58\)
- The population standard deviation is \(\sigma=100\)
- The desired margin of error is \(E = 35\)
\[n = \left(\frac{z_c \sigma}{E}\right)^2 \left(\frac{2.58\cdot 100}{35}\right)^2 = 54.34\]
Rounding up, the required sample size is at least 55.
Return back to Lesson 18.4