Practice
- A national education researcher wants to estimate the average SAT Math score for high school seniors in a particular state. The population standard deviation is known to be 100 points. What sample size is needed to get a margin of error less than 25 for a 92% confidence interval?
Solution
From the problem we get the following information:
- A confidence interval of 92% has a critical value of \(z_c = 1.75\)
- The population standard deviation is \(\sigma=100\)
- The desired margin of error is \(E = 25\)
\[n = \left(\frac{z_c \sigma}{E}\right)^2 \left(\frac{1.75\cdot 100}{25}\right)^2 = 49\]
Since this is an exact number, we don’t need to round up. The required sample size is at least 49.
Return back to Lesson 18.4