When Testing for a Difference Between the Means of a Treatment

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