Question

The average dividend yield of a random sample of 25 JSE-listed companies this year was found to be 14.5%, with a sample standard deviation of 3.4%. Assume that dividend yields are normally distributed. 3.1.1 Calculate, with 90% confidence, the actual mean dividend yield of all JSE-listed companies this year. Interpret the finding. (6) 3.1.2 Calculate, with 95% confidence, the actual mean dividend yield of all JSE-listed companies this year. Compare the interval with the one calculated in 3.1.1. (12

Answer 1

The half-interval for 90% CI is $z(0.95)*\frac{\sigma}{\sqrt{n}}$

$=1.645*\frac{3.4}{\sqrt{25}}\\ =1.12$

the interval is (13.4, 15.6) % yield units.

for 95% confidence z=1.96

the half- interval is 1.33

the interval is (13.2, 15.8) same units

More confidence, wider interval