Practice
- The average height of a particular species of flower is 5.5 inches with a standard deviation of 0.4 inches. You sample a subspecies and find 49 flowers with a sample mean height of 5.8 inches. What is the margin of error with a 95% confidence level?
We are given the population parameters:
- $\mu$ = 5.5
- $\sigma$ = 0.4
We are also given information about the sample:
The critical value for a 95% confidence level is 1.96. The margin of error then is,
\(E = z\frac{\sigma}{\sqrt{n}} = 1.96\frac{0.4}{\sqrt{49}} = \frac{1.96\cdot 0.4}{7} = \mathbf{0.112}\)
The confidence interval then is between the two values,
- $\bar{x} + E =$ 5.8 + 0.112 = 5.912
- $\bar{x} -SE =$ 5.8 - 0.112 = 5.688
Return back to Lesson 18.2