Test the Hypothesis That $\mu _ { 1 } > \mu _ { 2 }$

question 42

Essay

Test the hypothesis that $\mu _ { 1 } > \mu _ { 2 }$ . Two samples are randomly selected from each population. The sample statistics are given below. Use $\alpha = 0.01$ .
$$\begin{array} { l l } \mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 125 \\\overline { \mathrm { x } } 1 = 520 & \overline { \mathrm { x } } 2 = 505 \\\mathrm {~s} _ { 1 } = 45 & \mathrm {~s} _ { 2 } = 25\end{array}$$

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Definitions:

Hot Spot

A hot spot is a volcanic region thought to be fed by underlying mantle that is anomalously hot compared with the surrounding mantle.

Uplift

The geological process of rising segments of the Earth's crust, contributing to mountain formation and changes in topography.

Sierra Nevada Batholith

A large mass of igneous rock, primarily granite, located in the Sierra Nevada range, formed by the cooling of magma beneath the Earth's surface.

Ocean-Continent Convergence

A tectonic plate boundary situation where an oceanic plate is forced underneath a continental plate, often causing volcanic and seismic activity.