Question

The Chi-Square Table (Chapter 17)

The chi-square table: The degrees of freedom for a given test are listed in the column to the far left; the level of significance is listed in the top row to the right. These are the only two values you need to find the critical values for a chi-square test.

Increasing k and a in the chi-square table

13. Record the critical values for a chi-square test, given the following values for k at each level of significance: (3 points)

	.10	.05	.01
k = 10	___	___	___
k = 16	___	___	___
k = 22	___	___	___
k = 30	___	___	___

Note: Because there is only one k given, assume this is a goodness-of-fit test and compute the degrees of freedom as (k − 1).

14. As the level of significance increases (from .01 to .10), does the critical value increase or decrease? Explain.

15. As k increases (from 10 to 30), does the critical value increase or decrease? Explain you answer as it relates to the test statistic. (2 points)

Answer 1

Table:

	degrees of freedom=(k-1)	0.1	0.05	0.01
k=10	9	14.684	16.919	21.666
k=16	15	22.307	24.996	30.578
k=22	21	29.615	32.671	38.932
k=30	29	39.087	42.557	49.588

As the level of significance increases from 0.01 to 0.1 the critical values are decreasing. It means that the confidence level is decreasing when the critical values are decreasing.

As the ‘k’ values are increasing the critical values are increasing. It means that as increases sample size the critical values are increasing. Greater sample size gives significant results.