Question

a) The sample standard deviation of P/E ratios for stocks listed on the Sydney Stock Ex-change is s = 7.8. Assume that we are now interested in estimating the population mean P/E ratio for all stocks listed on the Sydney Stock Exchange in July 2004. How many stocks should be included in the sample if we want a margin of error of 2? Use a 95% confidence level.

Answer 1

The sample standard deviation of P/E ratios for stocks listed on the Sydney Stock Exchange is $s = 7.8$. Assume that we are now interested in estimating the population mean P/E ratio for all stocks listed on the Sydney Stock Exchange in July 2004. How many stocks should be included in the sample if we want a margin of error of 2? Use a 95% confidence level.

Solution

Here we have

$$s = 7.8, ME = 2, \text{Confidence interval} = 0.95, \text{critical value at } 5\% (z) = 1.96$$

We need to find the sample size:

$$n = \frac{s + s + z + z}{ME + ME} = \frac{7.8 + 7.8 + 1.96 + 1.96}{2 + 2} = 58$$

So we need 58 stocks should be included in the sample if we want a margin of error of 2.

Answer: 58 stocks