When Testing for a Difference Between the Means of a Treatment

question 131

Essay

When testing for a difference between the means of a treatment group and a placebo group, the computer display below is obtained. Using a 0.01 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 greater than the mean for the placebo population? Explain.
$$\begin{array} { | l | l | l | l | } \hline & \text { t-Test: Two Sample for Means } & & \\\hline 1 & & \text { Variable 1 } & \text { Variable 2 } \\\hline 2 & \text { Mean } & 171.6392 & 168.7718 \\\hline 3 & \text { Known Variance } & 47.51672 & 41.08293 \\\hline 4 & \text { Observations } & 50 & 50 \\\hline 5 & \text { Hypothesized Mean Difference } & 0 & \\\hline 6 & t & 2.154057 & \\\hline 7 & \text { P(T>=t) one-tail } & 0.0158 & \\\hline 8 & \text { TCritical one-tail } & 1.644853 & \\\hline 9 & \text { P(T?=t) two-tail } & 0.0316 & \\\hline 10 & t \text { Critical two-tail } & 1.959961 & \\\hline\end{array}$$

---

Definitions:

Concentration Ratio

A statistical measure that indicates the extent of competition in a market, calculated as the market share of the largest firms.

Economic Profits

The excess of total revenues over total costs, including both explicit and implicit costs, representing the profit beyond the normal return on investment.

Herfindahl Index

An economic indicator used to assess industry concentration by adding up the squares of individual firms' market shares, highlighting monopoly power.

Market Power

The ability of a firm or group of firms to control prices or exclude competition in a particular market.