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.
$$\begin{array} { | l | l | l | l | } \hline & \text { t-Test: Two Sample for Means } & & \\\hline 1 & & \text { Variable 1 } & \text { Variable 2 } \\\hline 2 & \text { Mean } & 171.6392 & 168.7718 \\\hline 3 & \text { Known Variance } & 47.51672 & 41.08293 \\\hline 4 & \text { Observations } & 50 & 50 \\\hline 5 & \text { Hypothesized Mean Difference } & 0 & \\\hline 6 & t & 2.154057 & \\\hline 7 & \text { P(T>=t) one-tail } & 0.0158 & \\\hline 8 & \text { TCritical one-tail } & 1.644853 & \\\hline 9 & \text { P(T?=t) two-tail } & 0.0316 & \\\hline 10 & t \text { Critical two-tail } & 1.959961 & \\\hline\end{array}$$

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Definitions:

Satiety

The feeling of being full or satisfied, typically in the context of eating, which reduces the desire to eat more food.

Drive Reduction

A theory in psychology suggesting that psychological needs create an aroused state that drives an organism to reduce that need by engaging in some goal-directed behavior.

Motivated Behaviors

Actions driven by internal desires and needs, such as hunger or achievement, guiding the organism towards specific goals.

Physiological Needs

Basic physical requirements including air, water, food, shelter, and sleep, necessary for survival.