You randomly draw a sample of n = 25 from a population where $\sigma$= 3. Which is the appropriate formula for the bounds of a 95% confidence interval?
A) $ \bar{x} \pm 1.960 * 0.6 $
B) $ \bar{x} \pm 1.645 * 0.6 $
C) $ \bar{x} \pm 1.960 * 0.12 $
D) $ \bar{x} \pm 1.645 * 0.12 $

Question

You randomly draw a sample of n = 25 from a population where $\sigma$= 3. Which is the appropriate formula for the bounds of a 95% confidence interval? 
A) $ \bar{x} \pm 1.960 * 0.6 $
B) $ \bar{x} \pm 1.645 * 0.6 $
C) $ \bar{x} \pm 1.960 * 0.12 $
D) $ \bar{x} \pm 1.645 * 0.12 $

Quizplus · Accepted Answer

The appropriate formula for a 95% confidence interval when the population standard deviation is known and the sample size is 25 is $ \bar{x} \pm z * \frac{\sigma}{\sqrt{n}} $. Here, $ z $ for 95% confidence is 1.960, $ \sigma = 3 $, and $ n = 25 $, so the standard error is $ \frac{3}{\sqrt{25}} = 0.6 $. Thus, the formula is $ \bar{x} \pm 1.960 * 0.6 $.

You Randomly Draw a Sample of N = 25 from a Population