A college offers both two-year and four-year programs of study. An administrator is investigating whether there is an association between the program of study and the length of the program. A random sample of students in all programs offered by the college was selected. All randomly selected students indicated their program of study and the length of the program. The results obtained are shown in the table.
Program of Study by Length of the Program
| Program of Study | Two-Year | Four-Year | Total |
|---|
| Liberal arts | 123 | 87 | 210 |
| Business | 315 | 145 | 460 |
| Health | 156 | 65 | 221 |
| Social sciences | 214 | 143 | 357 |
| Total | 808 | 440 | 1,248 |
The administrator wants to test the following hypotheses:
\(H_0:\) There is no association between the program of study and length of the program.
\(H_a:\) There is an association between the program of study and length of the program.
Assuming the conditions for inference have been met, the resulting test statistic was \( \chi^2 \approx 13.23 \).
At the 1 percent level of significance, which of the following is an appropriate conclusion of the test?
(A) The null hypothesis should not be rejected, and there is convincing statistical evidence of no association between the program of study and length of the program.
(B) The null hypothesis should not be rejected, and there is convincing statistical evidence of an association between the program of study and length of the program.
(C) The null hypothesis should not be rejected, and there is not convincing statistical evidence of an association between the program of study and length of the program.
(D) The null hypothesis should be rejected, and there is convincing statistical evidence of no association between the program of study and length of the program.
(E) The null hypothesis should be rejected, and there is convincing statistical evidence of an association between the program of study and length of the program.
