For a chi-square goodness-of-fit-test,the calculated chi-square value is 7.21.If the table chi-square value is 10.645,what is the appropriate decision for this test?
A)Reject the null hypothesis.
B)Fail to reject the null hypothesis.
C)Accept both the null and the alternative hypothesis.
D)It is impossible to determine anything from the given information.

Question

Quizplus · Accepted Answer

In a goodness-of-fit test, we compare the observed (actual) frequencies with the expected frequencies based on a theoretical distribution (null hypothesis). The null hypothesis assumes that there is no significant difference between the observed and expected frequencies. To test this hypothesis, we use the chi-square test statistic, which measures the degree of discrepancy between the observed and expected frequencies.

In this case, the calculated chi-square value is 7.21, which means that there is some discrepancy between the observed and expected frequencies, but it is not large enough to reject the null hypothesis. To make a decision, we compare the calculated chi-square value with the table chi-square value at a given level of significance and degrees of freedom. If the calculated chi-square value is less than the table chi-square value, we fail to reject the null hypothesis; otherwise, we reject the null hypothesis.

Since the table chi-square value is 10.645 and the calculated chi-square value is 7.21, we can see that the calculated value is less than the table value, which means that we fail to reject the null hypothesis. Therefore, the appropriate decision for this test is to fail to reject the null hypothesis.

For a Chi-Square Goodness-Of-Fit-Test,the Calculated Chi-Square Value Is 7