When Testing for a Difference Between the Means of a Treatment

question 16

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

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Definitions:

Compression

A force that acts to reduce volume or shorten a material, critical in the formation of geological structures.

Tension

A force that stretches a material, attempting to elongate it.

Shear

A strain resulting from forces causing parts of a material to slide past each other in opposite directions.

Confining

Pertaining to geological layers or conditions that restrict the flow of groundwater due to lower permeability.