When Testing the Difference Between the Means of a Treatment

question 24

Essay

When testing the difference between the means of a treatment group and a placebo group,the computer display below is obtained.Using a 0.05 significance level,is there sufficient evidence to support the claim that the treatment group (variable 1)represents a population whose mean is different from the mean for the untreated population? Explain. $$\begin{array} { | l | l | l | l | } \hline & \text { t-Test: Two Sample for Means } & & \\\hline 1 & & \text { Variable 1 } & \text { Variable } 2 \\\hline 2 & \text { Mean } & 65.10738 & 66.18251 \\\hline 3 & \text { Known V ariance } & 8.102938 & 10.27387 \\\hline 4 & \text { Observations } & 50 & 50 \\\hline 5 & \text { Hypothesized Mean Difference } & 0 & \\\hline 6 & \text { t } & - 1.773417 & \\\hline 7 & \text { P(T<=t) one-tail } & 0.0384 & \\\hline 8 & \text { TCritical one-tail } & 1.644853 & \\\hline 9 & \text { P(T<=t) two-tail } & 0.0768 & \\\hline 10 & \text { tCritical two-tail } & 1.959961 & \\\hline\end{array}$$

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Definitions:

Price Volatility

The rate at which the price of a security increases or decreases for a given set of returns, influencing the risk level of the security.

Bretton Woods Agreement

An international financial system established in 1944, creating fixed exchange rates, the International Monetary Fund (IMF), and the World Bank to promote global economic stability.

Price Volatility

The degree to which the price of an asset, security, or commodity fluctuates over time.