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:

Variable Costs

Expenses that change in proportion to the amount of goods produced or the volume of sales.

Fixed Cost

Costs that remain constant in total regardless of changes in the volume of activity or production level.

Cost Per Unit

The average cost to produce one unit of a product, calculated by dividing total production costs by the number of units produced.

Activity Level

A measure of the volume or quantity of work performed or production achieved in a specific period.