Test the Claim That $\mu _ { 1 } = \mu _ { 2 } .$

question 62

Essay

Test the claim that $\mu _ { 1 } = \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are
normally distributed. The sample statistics are given below. Assume that $\sigma _{ 1 } ^{ 2 } \neq \sigma _{ 2 } ^{ 2 } \text {. Use } \alpha = 0.05$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 25 & \mathrm { n } _ { 2 } = 30 \\\overline { \mathrm { x } _ { 1 } } = 18 & \overline { \mathrm { x } } _ { 2 } = 16 \\\mathrm {~s} _ { 1 } = 1.5 & \mathrm {~s} _ { 2 } = 1.9\end{array}$$

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Definitions:

Fragile X Syndrome

A genetic disorder causing intellectual disability, behavioral challenges, and characteristic physical features.

Phenylketonuria

A rare inherited disorder that increases the levels of a substance called phenylalanine in the blood, leading to intellectual disability and other health issues unless managed by diet from an early age.

Phenylalanine

An essential amino acid found in the human body used by the body to produce proteins and other important molecules, which is obtained through the diet.

Intellectual Disability

A disability characterized by significant limitations in both intellectual functioning and in adaptive behavior, which covers many everyday social and practical skills.