Poverty In a study of how the burden of poverty varies among U.S. regions, a random sample of 1000 individuals from each region of the United States recently yielded the information on poverty (based on defining the poverty level as an income below $10,400 for a family of 4 people). The data are provided in the table below. (All the conditions are satisfied - don't worry about checking them.)
$\begin{array}{|l|c|c|c|c|c|}
\hline& \text { Northwest } & \text { Midwest } & \text { South } & \text { West } & \text { Total } \
\hline \text { Poor } & 112 & 105 & 154 & 113 & 484 \
& (121) & (121) & (121) & (121) & \\hline \text { Not Poor } & \begin{array}{c}
888 \
(879)
\end{array} & \begin{array}{c}
895 \
(879)
\end{array} & \begin{array}{c}
846 \
(879)
\end{array} & \begin{array}{c}
887 \
(879)
\end{array} & 3516 \
\hline \text { Total } & 1000 & 1000 & 1000 & 1000 & 4000 \
\hline
\end{array}$

$\begin{array}{r}
\chi^{2}=\quad 0.67+2.12+9.00+0.53+ \
0.09+0.29+1.24+0.07+ \
=14.01
\end{array}$
$P=0.0029$
a. Write appropriate hypotheses.
b. How many degrees of freedom?
c. Suppose the expected values had not been given. Show exactly how to calculate the expected count in the first cell.
d. State your complete conclusion in context.

Question

Poverty In a study of how the burden of poverty varies among U.S. regions, a random sample of 1000 individuals from each region of the United States recently yielded the information on poverty (based on defining the poverty level as an income below $10,400 for a family of 4 people). The data are provided in the table below. (All the conditions are satisfied - don't worry about checking them.) 
$\begin{array}{|l|c|c|c|c|c|}
\hline& \text { Northwest } & \text { Midwest } & \text { South } & \text { West } & \text { Total } \
\hline \text { Poor } & 112 & 105 & 154 & 113 & 484 \
& (121) & (121) & (121) & (121) & \\hline \text { Not Poor } & \begin{array}{c}
888 \
(879)
\end{array} & \begin{array}{c}
895 \
(879)
\end{array} & \begin{array}{c}
846 \
(879)
\end{array} & \begin{array}{c}
887 \
(879)
\end{array} & 3516 \
\hline \text { Total } & 1000 & 1000 & 1000 & 1000 & 4000 \
\hline
\end{array}$

$\begin{array}{r}
\chi^{2}=\quad 0.67+2.12+9.00+0.53+ \
0.09+0.29+1.24+0.07+ \
=14.01
\end{array}$
$P=0.0029$ 
a. Write appropriate hypotheses.
b. How many degrees of freedom?
c. Suppose the expected values had not been given. Show exactly how to calculate the expected count in the first cell.
d. State your complete conclusion in context.

Quizplus · Accepted Answer

The Answer is a.

\mathrm { H } _ { 0 }

: Poverty percentages are the same for the geographic regions in the Unites States.

\mathrm { H } _ { \mathrm { A } }

: Poverty percentages differ by geographic region in the United States.
b. degrees of freedom

= ( 4 - 1 ) ( 2 - 1 ) = 13

c.

\frac { 1000 } { 4 000 } ( 484 ) = 121

d. Since the

P

-value of

0.0029

is so low, there is strong evidence that poverty percentages differ by geographic location in the United States. We will reject the null hypothesis and conclude that poverty is associated with geographic location in the United States. Specifically, the South contains a greater proportion of people below the poverty level than expected.

Poverty in a Study of How the Burden of Poverty