To determine the conclusion about the null hypothesis, we need to compare the computed test statistic to the critical value.
1. State the given information:
- The test statistic value is [tex]\(\chi^2 = 0.579\)[/tex].
- The critical value is [tex]\(\chi^2 = 5.991\)[/tex].
2. Formulate the decision rule:
- The null hypothesis ([tex]\(H_0\)[/tex]) will be rejected if the test statistic is greater than or equal to the critical value.
- Conversely, if the test statistic is less than the critical value, we fail to reject the null hypothesis.
3. Compare the test statistic to the critical value:
[tex]\[
\chi^2 = 0.579 < 5.991
\][/tex]
4. Draw the conclusion:
Since the test statistic ([tex]\(0.579\)[/tex]) is less than the critical value ([tex]\(5.991\)[/tex]), we fail to reject the null hypothesis ([tex]\(H_0\)[/tex]). This means that there is not sufficient evidence to conclude that college graduation status and cola preference are dependent.
Thus, we conclude:
A. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that college graduation status and cola preference are independent.
