Question

The following are the hypotheses for a test of the claim that college graduation statue and cola preference are independent. H0: College graduation status and cola preference are independent. H1: College graduation status and cola preference are dependent. If the test statistic: χ2 = 0.579 and the critical value is χ2 = 5.991, what is your conclusion about the null hypothesis and about the claim?

Answer 1

Answer:

$\chi^2 = 0.579$

And the critical value for the significance level used is:

$\chi^2_{crit}= 5.991$

Since the calculated value is less than the critical value we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the College graduation status and cola preference are independent

Step-by-step explanation:

For this case we want to test the following hypothesis:

Null hypothesis: College graduation status and cola preference are independent

Alternative hypothesis: College graduation status and cola preference are dependent

For this case we got a calculated statistic of:

$\chi^2 = 0.579$

And the critical value for the significance level used is:

$\chi^2_{crit}= 5.991$

Since the calculated value is less than the critical value we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the College graduation status and cola preference are independent

Answer 2

Critical value (5.991) is greater than the test statistic (0.579).

We would accept the null hypothesis (H0) which says, "College graduation status and cola preference are independent". This means that the claim TRUE.

Recall the following about decision making when rejecting or accepting an hypothesis:

• When the critical value is greater than the test statistic, we accept the null hypothesis (H0) and reject the alternative hypothesis (H1).

• When the critical value is less than the test statistic, we reject the null hypothesis (H0) and accept the alternative hypothesis (H1).

Thus, the information given shows that:

Critical value (5.991) is greater than the test statistic (0.579).

• Therefore, we would accept the null hypothesis (H0) which says, "College graduation status and cola preference are independent". This means that the claim TRUE.

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