A Statistician Wants to Test for the Equality of Means

question 45

Essay

A statistician wants to test for the equality of means in two independent samples drawn from normal populations. However, he will not perform the equal-variance t-test of the difference between the population means if the condition necessary for its use is not satisfied. The data are as follows: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | l | } \hline \text { Sample 1: } & 7 & 9 & 6 & 15 & 7 & 10 & 8 & 12 & & \\\hline \text { Sample 2: } & 2 & 25 & 9 & 15 & 10 & 18 & 5 & 22 & 27 & 3 \\\hline\end{array}$$ Estimate with 95% confidence the ratio of the two population variances.

---

Definitions:

Treynor-Black Model

An optimization tool used by portfolio managers to balance the trade-off between risk and return by combining actively selected securities with a passively managed market portfolio.

Nonsystematic Risk

The risk associated with a specific issuer of a security, industry, or sector, which can be mitigated through diversification.

Systematic Risk

The risk inherent to the entire market or entire market segment, which cannot be mitigated through diversification.

Purely Passive Strategy

An investment strategy that involves no active management and typically focuses on investing in index funds to replicate market returns.