When Testing for a Difference Between the Means of a Treatment

question 35

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 0.04 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.
$$\begin{array} { | l | l | l | l | } \hline & \text { t-Test: Two Sample for Means } & & \\\hline 1 & & \text { Variable 1 } & \text { Variable 2 } \\\hline 2 & \text { Mean } & 171.6392 & 168.7718 \\\hline 3 & \text { Known Variance } & 47.51672 & 41.08293 \\\hline 4 & \text { Observations } & 50 & 50 \\\hline 5 & \text { Hypothesized Mean Difference } & 0 & \\\hline 6 & \mathrm { t } & 2.154057 & \\\hline 7 & \text { P(T>=t) one-tail } & 0.0158 & \\\hline 8 & \text { TCritical one-tail } & 1.644853 & \\\hline 9 & \text { P(T>=t) two-tail } & 0.0316 & \\\hline 10 & \mathrm { t } \text { Critical two-tail } & 1.959961 & \\\hline\end{array}$$

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Definitions:

Attitude

A psychological tendency expressed by evaluating a particular entity with some degree of favor or disfavor.

Type A Personality

A personality type characterized by high levels of competitiveness, self-imposed stress, and a constant sense of urgency.

Antagonistic Hostility

Aggressive feelings or actions that are oppositional or unfriendly in nature.

Primary Control

The ability to directly influence and manipulate one's environment or circumstances to achieve one's goals.