# Why isn't the chi-squared test appropriate in this case?

I was trying to solve the following exercise:

Two researchers studied the relationship between infant mortality and environmental conditions in Dauphin County, Pennsylvania. As a part of the study, the researchers recorded, for each baby born in Dauphin Country during a six-month period, in what season the baby was born, and whether or not the baby died before reaching one year of age. If appropriate, test to see whether infant mortality depends on season of birth. If a test is not appropriate, explain why not.

For Jul-Aug-Sept: 35 died before one year and 958 lived at least one year

For Oct-Nov-Dec: 7 died before one year and 990 lived at least one year

According to the answers in the book there is no appropriate test:

A test of significance is not appropriate here, unless a box model can be specified for the data

But why cannot I just perform the chi-squared test of independence for (2-1)(2-1)=1 degree of freedom? If I calculated the expected values in the way required for this test, wouldn't be this the same as giving a box model for the null hypothesis saying that there is no dependence?

• It is true that a chi-sq test and a Fisher exact test both 'reject' the $H_0$ of equal death rates in the 2 seasons. But any inference might be valid only for Dauphin Cnty and only for the 6-mo period in question--and only if deaths occurred independently, // Were time and place selected specifically because of unusually high death rate? Might some summer deaths have been due to a common cause? // For me at least, you'd need to explain the relevance of "box model." // More appropriate to choose about 2000 births at random from US over several yrs, Then look for different death rates by season. – BruceET May 14 at 16:50