Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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 :

GinnyAnswer
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.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.