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# Correct Hypotheses: Heights of Twins

APSTAT-YB0GQB

A random sample on heights of $50$ pairs of $18$ year old identical twins was used to determine whether the second born twin tends to be taller than the first born.

Let ${ \mu }_{ 2 }$ represent the average height of the second born, let ${ \mu }_{ 1 }$ represent the average height of the first born twin, and let ${ \mu }_{ d }$ represents the average difference in the height (height of second born minus height of first born) for all pairs of twins.

Which of the following would be the null and alternative hypothesis for this study?

A

${ H }_{ 0 }:\quad { \mu }_{ d }=0\\\ { H }_{ a }:\quad { \mu }_{ d }>0$

B

${ H }_{ 0 }:\quad { \mu }_{ d }=0\\\ { H }_{ a }:\quad { \mu }_{ d }<0$

C

${ H }_{ 0 }:\quad { \mu }_{ 2 }={ \mu }_{ 1 }\\\ { H }_{ a }:\quad { \mu }_{ 2 }>{ \mu }_{ 1 }$

D

${ H }_{ 0 }:\quad { \mu }_{ 2 }={ \mu }_{ 1 }\\\ { H }_{ a }:\quad { \mu }_{ 2 }<{ \mu }_{ 1 }$

E

${ H }_{ 0 }:\quad { \mu }_{ 2 }-{ \mu }_{ 1 }={ \mu }_{ D }\\\ { H }_{ a }:{ \quad \mu }_{ 2 }-{ \mu }_{ 1 }>{ \mu }_{ D }$