Use the Computer Display to Solve the Problem

question 70

Essay

Use the computer display to solve the problem.
-When testing for a difference between the means of a treatment group and a placebo group, the computer display below is obtained. Using a 0.04 significance level, is there sufficient evidence to support the claim that the treatment group (variable 1)comes from a population with a mean that is different from the mean for the placebo population? Explain. $$\begin{array} { | l | l | l | l | } \hline & \text { t-Test: Two Sample for Means } & & \\\hline 1 & & \text { Variable 1 } & \text { Variable 2 } \\\hline 2 & \text { Mean } & 171.6392 & 168.7718 \\\hline 3 & \text { Known Variance } & 47.51672 & 41.08293 \\\hline 4 & \text { Observations } & 50 & 50 \\\hline 5 & \text { Hypothesized Mean Difference } & 0 & \\\hline 6 & \text { t } & 2.154057 & \\\hline 7 & \text { P(T>=t) one-tail } & 0.0158 & \\\hline 8 & \text { TCritical one-tail } & 1.644853 & \\\hline 9 & \text { P(T>=t) two-tail } & 0.0316 & \\\hline 10 & \text { tCritical two-tail } & 1.959961 & \\\hline\end{array}$$

---

Definitions:

Information Ratio

A measure of a portfolio manager's performance and ability to generate excess returns relative to a benchmark, considering the volatility of those returns.

Residual Standard Deviation

This is a measure used in statistics to estimate the standard deviation of the residuals (errors) from a regression line, indicating how well the model fits the data.

Beta

A measure of a security's volatility in relation to the overall market; used as a gauge of its risk.

T-Bills

Short-term government securities issued at a discount from par value and maturing at face value, providing a return in the form of the difference between the purchase price and the maturity value.