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Hypotheses About Young Voters

APSTAT-78OBPH

According to media reports, a certain political candidate has a higher rate of support among "young" voters (those age $30$ and under) than "older" voters (those over the age of $30$). A researcher wanted to investigate whether the media reports were true. To gather data, he selected a random sample of $200$ "young" voters and a random sample of $200$ "older" voters and asked if they supported the political candidate.

Which of the following hypotheses could the researcher use to determine if the media claims are true?

A

${ H }_{ 0 }:\quad \hat { { p }_{ Y } } >0.50 $

The proportion of young voters who support the candidate is greater than $0.50$.

${ H }_{ a }:\quad \hat { { p }_{ O } } <0.50$

The proportion of older voters who support the candidate is less than $0.50$.

B

${ H }_{ o }:\quad \hat { { p }_{ Y } } =\hat { { p }_{ O } }$

The proportion of "young" voters who support the candidate is equal to the proportion of "older" voters who support the candidate.

${ H }_{ a }:\quad \hat { { p }_{ Y } } <\hat { { p }_{ O } } $

The proportion of "young" voters who support the candidate is less than the proportion of "older" voters who support the candidate.

C

${ H }_{ o }:\quad { { p }_{ Y } } = { { p }_{ O } }$

The proportion of "young" voters who support the candidate is equal to the proportion of "older" voters who support the candidate.

${ H }_{ a }:\quad { { p }_{ Y } } > { { p }_{ O } } $

The proportion of "young" voters who support the candidate is greater than the proportion of "older" voters who support the candidate.

D

${ H }_{ o }:\quad { { p }_{ Y } } = { { p }_{ O } }$

The proportion of "young" voters who support the candidate is equal to the proportion of "older" voters who support the candidate.

${ H }_{ a }:\quad { { p }_{ Y } }\neq { { p }_{ O } } $

The proportion of "young" voters who support the candidate is not equal to the proportion of "older" voters who support the candidate.

E

${ H }_{ o }:\quad { { \mu}_{ Y } } = { { \mu }_{ O } }$

The mean number of "young" voters who support the candidate is equal to the mean number of "older" voters who support the candidate.

${ H }_{ a }:\quad { { \mu}_{ Y } } > { { \mu}_{ O } } $

The mean number of "young" voters who support the candidate is greater than the mean number of "older" voters who support the candidate.