In a chi-squared test of a contingency table, the value of the test statistic was =12.678, and the critical value at = 0.025 was 14.4494. Thus, (Points: 2)
A) we fail to reject the null hypothesis at = 0.025
B) we reject the null hypothesis at = 0.025
C) we don’t have enough evidence to accept or reject the null hypothesis at = 0.025
D) we should decrease the level of significance in order to reject the null hypothesis
If the test statistic does not exceed the value for P = .025, then you cannot reject the null hypothesis (A).
However, you have not given the degrees of freedom
(df) for the table. I am assuming that the critical value is for the appropriate df. If not, then C is the answer.
Well, if the chi-squared test statistic (12.678) is less than the critical value (14.4494), it means we don't have enough evidence to reject the null hypothesis. So, C) we don't have enough evidence to accept or reject the null hypothesis at = 0.025. The test statistic just didn't make the cut. Maybe it needs a few more comedy lessons to improve its performance!
The correct answer is A) we fail to reject the null hypothesis at = 0.025.
In a chi-squared test, we compare the observed frequencies in a contingency table with the expected frequencies under the assumption of independence between the variables. The test statistic measures the deviation from independence.
To make a decision, we compare the test statistic with the critical value from the chi-squared distribution at the desired significance level ( = 0.025 in this case). If the test statistic is greater than the critical value, we reject the null hypothesis, indicating that there is evidence of a relationship between the variables. However, if the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis, indicating that there is not enough evidence to conclude a relationship between the variables.
Here, the test statistic value of 12.678 is less than the critical value of 14.4494. Therefore, we fail to reject the null hypothesis at = 0.025.
To determine which option is correct, we need to compare the test statistic value with the critical value.
In the chi-squared test, the null hypothesis assumes that there is no relationship between the variables being tested. The alternative hypothesis assumes that there is a relationship between the variables.
To make a decision about the null hypothesis, we compare the test statistic to the critical value. If the test statistic is less than the critical value, we fail to reject the null hypothesis. If the test statistic is greater than the critical value, we reject the null hypothesis.
In this case, the test statistic is 12.678, and the critical value at α = 0.025 is 14.4494.
Since the test statistic (12.678) is less than the critical value (14.4494), we fail to reject the null hypothesis. This means that we do not have enough evidence to suggest a relationship between the variables being tested.
Thus, the correct answer is option A) we fail to reject the null hypothesis at α = 0.025.