When Testing the Difference Between the Means of a Treatment

question 24

Essay

When testing the 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)represents a population whose mean is different from the mean for the untreated population? Explain. $$\begin{array} { | l | l | l | l | } \hline & \text { t-Test: Two Sample for Means } & & \\\hline 1 & & \text { Variable 1 } & \text { Variable } 2 \\\hline 2 & \text { Mean } & 65.10738 & 66.18251 \\\hline 3 & \text { Known V ariance } & 8.102938 & 10.27387 \\\hline 4 & \text { Observations } & 50 & 50 \\\hline 5 & \text { Hypothesized Mean Difference } & 0 & \\\hline 6 & \text { t } & - 1.773417 & \\\hline 7 & \text { P(T<=t) one-tail } & 0.0384 & \\\hline 8 & \text { TCritical one-tail } & 1.644853 & \\\hline 9 & \text { P(T<=t) two-tail } & 0.0768 & \\\hline 10 & \text { tCritical two-tail } & 1.959961 & \\\hline\end{array}$$

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Definitions:

Benign

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Cigarette Smoking

The act of inhaling and exhaling the smoke of burning tobacco, typically contained in cigarettes, which is a major risk factor for numerous health issues.

Cardiovascular Disease

A class of diseases that involve the heart or blood vessels, such as coronary artery disease, hypertension, heart failure, and stroke, leading causes of death globally.

Type A Behavior

A pattern of behaviors and personality traits characterized by high levels of competitiveness, impatience, aggressiveness, and a constant sense of urgency.