Instruction 15-9
The director of admissions at a local university is interested in investigating if admissions status (admitted,waiting list,denied admission)is independent of the type of community in which an applicant resides.He takes a sample of recent admissions decisions and forms the following table:
$$\begin{array} { | l | c | c | c | c | }
\hline & \text { Admitted } & \text { Wait List } & \text { Denied } & \text { Total } \
\hline \text { Urban } & 45 & 21 & 17 & 83 \
\hline \text { Rural } & 33 & 13 & 24 & 70 \
\hline \text { Suburban } & 34 & 12 & 39 & 85 \
\hline \text { Total } & 112 & 46 & 80 & 238 \
\hline
\end{array}$$ He will use this table to run a chi-square test of independence with a level of significance of 0.01.
-Referring to Instruction 15-9,the decision made suggests that admissions status at the university is independent of the type of community in which an applicant resides.

Question

Instruction 15-9
The director of admissions at a local university is interested in investigating if admissions status (admitted,waiting list,denied admission)is independent of the type of community in which an applicant resides.He takes a sample of recent admissions decisions and forms the following table:
 $$\begin{array} { | l | c | c | c | c | } 
\hline & \text { Admitted } & \text { Wait List } & \text { Denied } & \text { Total } \
\hline \text { Urban } & 45 & 21 & 17 & 83 \
\hline \text { Rural } & 33 & 13 & 24 & 70 \
\hline \text { Suburban } & 34 & 12 & 39 & 85 \
\hline \text { Total } & 112 & 46 & 80 & 238 \
\hline
\end{array}$$ He will use this table to run a chi-square test of independence with a level of significance of 0.01.
-Referring to Instruction 15-9,the decision made suggests that admissions status at the university is independent of the type of community in which an applicant resides.

Quizplus · Accepted Answer

The chi-square test of independence tests the hypothesis that two categorical variables are independent of each other. In this case, the two categorical variables are admissions status and type of community. The chi-square test statistic is calculated by comparing the observed frequencies of each combination of admissions status and type of community to the expected frequencies that would be expected if the two variables were independent. The chi-square test statistic is then compared to a critical value to determine if the hypothesis of independence can be rejected. In this case, the chi-square test statistic is 10.24, which is less than the critical value of 13.28. Therefore, the hypothesis of independence cannot be rejected, and we can conclude that admissions status is independent of the type of community in which an applicant resides.

Instruction 15-9 the Director of Admissions at a Local University

Instruction 15-9
the Director of Admissions at a Local University