I have a little trouble understanding the results of a $\chi^2$ test. I have the following statistics about people suffering accidents treated at hospitals or clinics.
| dies | survives
hospital | 53 | 218
clinic | 46 | 825
Based on the lecture notes Excel computes $53.2$ for $\chi^2$ value from the table. The degree of freedom is $1$, level of confidence is $5%$, the expected $\chi^2$ value is $3.841.$ Because $53.2$ is greater than $3.841$, the null hypothesis is invalid, so - what does it mean? The chance of surviving is not independent of the place of treatment? Common sense from the data suggest that patients in the clinic have better chances, so it seems right and I think I understand this example.
However, I have an other example about coffee consumption and marital status:
consumed coffee (mg/day)
| 0 | 1-150 | 151-300 | >300
married | 678 | 1567 | 612 | 253
divorced | 69 | 121 | 102 | 86
single | 284 | 344 | 163 | 97
I did the same calculations with Excel and got $157.9$ for $\chi^2$. The degree of freedom is $6$, level of confidence is $5%$, the expected $\chi^2$ value is $12.59.$ Because $157.9$ is greater than $12.59$, the null hypothesis is invalid, so - what does it mean? The coffee consumption is not independent of marital status? Married people are less likely to drink $151+$ mg/day coffee than divorced people?