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The following are the hypotheses for a test of the claim that college graduation status and cola preference are independent.

[tex]\[ H_0: \text{College graduation status and cola preference are independent.} \][/tex]
[tex]\[ H_1: \text{College graduation status and cola preference are dependent.} \][/tex]

If the test statistic is [tex]\(\chi^2 = 0.579\)[/tex] and the critical value is [tex]\(\chi^2 = 5.991\)[/tex], what is your conclusion about the null hypothesis and the claim?

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.

B. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that college graduation status and cola preference are independent.

C. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that college graduation status and cola preference are independent.

D. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that college graduation status and cola preference are independent.

Sagot :

GinnyAnsweridn
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.
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