TABLE 12-10
The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college 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:
$$\begin{array} { l | l l l | l }
& \text { Admitted } & \text { Wait List } & \text { Denied } & \text { Total } \
\hline \text { Urban } & 45 & 21 & 17 & 83 \
\text { Rural } & 33 & 13 & 24 & 70 \
\text { Suburban } & 34 & 12 & 39 & 85 \
\hline \text { Total } & 112 & 46 & 80 & 238
\end{array}$$ He will use this table to do a chi-square test of independence with a level of significance of 0.01.
-Referring to Table 12-10, the same decision would be made with this test if the level of significance had been 0.005.

Question

TABLE 12-10
The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college 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:
 $$\begin{array} { l | l l l | l } 
& \text { Admitted } & \text { Wait List } & \text { Denied } & \text { Total } \
\hline \text { Urban } & 45 & 21 & 17 & 83 \
\text { Rural } & 33 & 13 & 24 & 70 \
\text { Suburban } & 34 & 12 & 39 & 85 \
\hline \text { Total } & 112 & 46 & 80 & 238
\end{array}$$ He will use this table to do a chi-square test of independence with a level of significance of 0.01.
-Referring to Table 12-10, the same decision would be made with this test if the level of significance had been 0.005.

Quizplus · Accepted Answer

The chi-square test of independence is a non-parametric test that is used to determine whether there is a significant relationship between two categorical variables. The level of significance is the probability of rejecting the null hypothesis when it is actually true. In this case, the null hypothesis is that there is no relationship between admissions status and type of community. The level of significance of 0.01 means that there is a 1% chance of rejecting the null hypothesis when it is actually true. The chi-square test statistic is calculated by comparing the observed frequencies of the data to the expected frequencies under the null hypothesis. The expected frequencies are calculated by multiplying the row totals by the column totals and dividing by the grand total. The chi-square test statistic is then calculated by summing the squared differences between the observed and expected frequencies and dividing by the expected frequencies. The resulting value is compared to a critical value from a chi-square distribution with (r-1) * (c-1) degrees of freedom, where r is the number of rows and c is the number of columns in the contingency table. If the chi-square test statistic is greater than the critical value, then the null hypothesis is rejected and it is concluded that there is a significant relationship between the two variables. In this case, the chi-square test statistic is 12.06, which is greater than the critical value of 10.83 with 4 degrees of freedom. Therefore, the null hypothesis is rejected and it is concluded that there is a significant relationship between admissions status and type of community. The same decision would be made with this test if the level of significance had been 0.005 because the chi-square test statistic is still greater than the critical value of 12.59 with 4 degrees of freedom.

TABLE 12-10 the Director of Admissions at a State College

TABLE 12-10
the Director of Admissions at a State College