Consider the following hypothesis problem. The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)
A) 42.557.
B) 43.773.
C) 16.047 and 45.722.
D) 16.791 and 46.979.

Question

​Consider the following hypothesis problem.  ​ ​The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)
A) ​42.557. 
B) ​43.773. 
C) ​16.047 and 45.722. 
D) ​16.791 and 46.979.

Quizplus · Accepted Answer

Without knowing the degrees of freedom or the value of the test statistic, it is impossible to determine the exact critical value. However, because the chi-square distribution table includes different critical values for different levels of significance and degrees of freedom, we can eliminate options A and B simply by noting that their values are too large to correspond to a 5% level of significance. Option D includes values that may be too small to correspond to a 5% level of significance. Therefore, option C, which includes two critical values that bracket the possible values of the test statistic, is the best choice.

​Consider the Following Hypothesis Problem

Consider the Following Hypothesis Problem