When Testing for a Difference Between the Means of a Treatment

question 42

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 0.05 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 less than the mean for the placebo population? Explain. $\text { t-Test: Two Sample for Means }$
$\begin{array} { | l | l | l | l | } \hline 1 & & \text { Variable 1 } & \text { Variable } 2 \\\hline 2 & \text { Mean } & 65.10738 & 66.18251 \\\hline 3 & \text { Known Variance } & 8.102938 & 10.27387 \\\hline 4 & \text { Observations } & 50 & 50 \\\hline 5 & \text { Hypothesized Mean Difference } & 0 & \\\hline 6 & t & - 1.773417 & \\\hline 7 & P ( T < = t ) \text { one-tail } & 0.0384 & \\\hline 8 & T \text { Critical one-tail } & 1.644853 & \\\hline 9 & P ( T < = t ) \text { two tail } & 0.0768 & \\\hline 10 & t \text { Critical two-tail } & 1.959961 & \\\hline\end{array}$

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Definitions:

Production Possibility Frontier

A curve depicting all maximum output possibilities for two or more goods given a set of inputs (resources, labor, etc.).

Trade

Conducting transactions involving the exchange, sale, or purchase of goods and services by or among people and countries.

Consuming Outside

The act of purchasing and enjoying goods or services outside one’s home, such as dining at restaurants or outdoor markets.

Opportunity Cost

The sacrifice involved in not picking the subsequent preferable option at the time of decision-making.