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

Question

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

Quizplus · Accepted Answer

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

When Testing for a Difference Between the Means of a Treatment