A Small Private College Is Interested in Determining the Percentage $\begin{array} { l l } \text { Sample Size } & 108 \\ \text { Successes } & 16 \\ \text { Proportion } & 0.14815 \end{array}$

question 96

Short Answer

A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. A sample of 108 students was randomly selected and the following printout was obtained: Hypothesis Test - One Proportion
$\begin{array} { l l } \text { Sample Size } & 108 \\ \text { Successes } & 16 \\ \text { Proportion } & 0.14815 \end{array}$

Null Hypothesis: $\quad P = 0.2$
Alternative Hyp: $\quad P < 0.2$

Difference $\quad - 0.05185$
Standard Error $\quad 0.03418$

$\begin{array} { l l l l } \mathrm { Z } & - 1.35 & \mathrm { p } \text {-value } & 0.0885 \end{array}$ Based on the information contained in the printout, what conclusion would be correct when testing at α = 0.05. A) Reject $\mathrm { H } _ { 0 }$
B) Fail to reject $\mathrm { H } _ { 0 }$
C) Accept $\mathrm { H } _ { 0 }$
D) Accept $\mathrm { H } _ { \mathrm { A } }$

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Definitions:

Market Basket Measure

A benchmark of income poverty that estimates the cost of a specific set of goods and services representing a modest, basic standard of living.

Low-Income Cut-Off

A statistical threshold under which a family unit would be considered to be living in relative poverty, defined by their income.

Low-Income Measure

A statistical threshold used to identify individuals or families that earn significantly less than the average in their society, often used to target social support.

Intergenerational Poverty

Often occurs when children and youth grow up in households experiencing chronic poverty, where limited access to opportunities can start another cycle of poverty for the next generation.