Often frequency data are tabulated according to two categories to decide if there is a relationship between categories and counts, in other words. Do the categories matter? Machine shop Hi-Tech errors are tabulated by Shift and Machine with significance level in Table 1.1. Are the machines and shifts operating consistently? Perform the appropriate test.

Table 1.1

ALPHA =	0.05
		Shift
		1	2	3
Machine	A	8	11	7
B	11	6	6
C	7	7	26
D	8	7	21
E	10	10	20
F	7	7	22
G	8	7	8
H	7	10	6

1. The chi square statistic 24.375 does not exceed the critical value 29.14 and fails to reject H0.
2. The pvalue 0.018 < is significant evidence against H0, rejects H0, and action is needed to improve machine errors.
3. The chi square statistic 3.085 does not exceeds the critical value 23.68 and fails to reject H0.
4. The pvalue 0.074 < is significant evidence against H0, rejects H0, and action is needed to improve machine errors.
5. The chi square statistic 17.554 does not exceeds the critical value 21.06 and fails to reject H0.
6. None of the answers match my chi square results.