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:

Facial Expression

The arrangement and movement of the facial muscles to convey emotion, information, or reactions.

Brows Raised

A facial expression where the eyebrows are lifted upwards, often indicating surprise, curiosity, or questioning.

Eyes Widened

A physical reaction where the eyelids open more than usual, often in response to surprise, shock, or intense focus.

Mouth Rounded

Describes the shape and position of the lips when forming certain speech sounds, often contrasted with lip spreading or neutral positions.