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Marital Status: Find the $p$-Value

APSTAT-231G1G

The table below displays the marital status of people age 15 and over as reported by the U. S. Census Bureau (2012).

Marital Status Percent
Married 50.7
Never Married 31.2
Divorced 10.1
Widowed 5.7
Separated 2.1



Tabitha wonders whether this distribution accurately represents people in her town. To investigate, she selects $90$ adults that she meets in the town library, explains that she is doing a statistical study, and asks them to describe their marital status. Of those she surveyed, $50$ said they were married, $21$ said they were never married, $14$ said they were divorced, $3$ said they were widowed, and $2$ said they were separated.

Tabitha realizes that people who are at the library may in some ways be similar, but she is willing to accept that her sample was randomly selected. Also, she has already determined that all other conditions for performing her hypothesis test have been satisfied.

What $p$-value will Tabitha obtain from her test?

A

$0.125$

B

$0.219$

C

$0.332$

D

$0.453$

E

A value that is nearly equal to $1$