2020 ACJC P2 Q10

A popular investment manager claims that the mean dividend yield of his clients is \(12\%\). A research firm investigates further by collecting a random sample of \(40\) of the manager’s clients. The sample was found to have a mean dividend yield of \(10.9\%\) and a standard deviation of \(2.5\%\)

1. State, giving a reason, whether there is a need to make any assumption about the distribution of the dividend yield earned by the manager’s clients in order for a hypothesis test to be valid.[1]
2. Test, at the \(5%\) level of significance, whether the manager overstated his claim.[5]

It was later known that the standard deviation of the dividend yield of the popular investment manager’s clients is \(2.3\%\). A potential investor collected the dividend yield data of a small sample size, \(n\), of the manager’s clients. The sample was found to have a mean dividend yield of \(10.2\%\).

3. State, in context, two assumptions that are needed for you to carry out a test to examine the manager’s claim that the mean dividend yield of his clients is \(12\%\).[2]
4. Hence find the least value of \(n\) such that the manager’s claim at the \(5\%\) level of significance, will be rejected. You should state your hypothesis clearly.[4]