Question

What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories? Select one: a. 3.841 b. 5.991 c. 7.815 d. 11.070

Answer 1

Answer:

The correct option is (d) 11.070

Step-by-step explanation:

The test statistic for Goodness of fit test for k observations is:

$\chi^{2}=\sum\frac{(Observed-Expected)^{2}}{Expected}$

This statistic follows a Chi-square distribution with (k - 1) degrees of freedom and α level of significance.

Here α = 0.05 and degrees of freedom is, k - 1 = 6 - 1 = 5 d.f.

Use the chi-square table for the critical value.

$\chi^{2}_{(5)}=11.070$

Thus, the correct option is (d).