Assume That the Two Samples Are Independent Simple Random Samples

question 33

Essay

Assume that the two samples are independent simple random samples selected from normally
distributed populations. Do not assume that the population standard deviations are equal. A
researcher wishes to determine whether people can reduce their resting heart rate by following
a particular diet. Construct a 95% confidence interval estimate for the following data. Does
the confidence interval support that the mean resting heart rate for those on the diet is lower
than that of those not on the diet? Explain your reasoning. $$\begin{array} { | l | l | } \hline \text { Treatment Group } &{ \text { Control Group } } \\\hline n _ { 1 } = 35 & n _ { 2 } = 38 \\\hline \bar { x } _ { 1 } = 79.1 & \bar { x } _ { 2 } = 84.7 \\\hline s _ { 1 } = 8.7 & s _ { 2 } = 9.2 \\\hline\end{array}$$

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Definitions:

Natural Selection

A process in evolutionary biology where organisms better adapted to their environment tend to survive and produce more offspring.

Passing on Genes

The biological process through which an individual transmits genetic information to their offspring, contributing to the genetic makeup of successive generations.

Evolutionary Psychology

A theoretical approach in psychology that examines mental structure from a modern evolutionary perspective, focusing on how evolutionary principles such as natural selection have shaped the mind and behavior.

William James

An American philosopher and psychologist, often referred to as the father of American psychology, known for his works on pragmatism and functionalism.