Question

The 189 births from the study in the last question are cross-tabulated below with respect to mother’s race and if the birth was LBW or not.  A chi-square statistic was calculated to test whether or not “race” was independent of LBW. The result was a calculated value of 8.20

		LBW
		No	Yes	total
Race	White	76	20	96
	Black	14	12	26
	Other	43	24	67
	total	133	56	189

1. The degrees of freedom associated this chi-square statistic = [a].
2. The critical chi-square value, beyond which 5% of the chi-square distribution lies (α=0.05) = [b]. (round to 2 decimal places, such as 1.23)
3. Is there is a significant association between race and LBW based on the α=0.05 test (does 8.20 exceed the critical value?). (type yes or no) [c]

Answer 1

Solution:

Given: A chi-square statistic was calculated to test whether or not “race” was independent of LBW.

The result was a calculated value of 8.20

that is:

Part a) The degrees of freedom associated this chi-square statistic = [a].

We have R = Number of Rows = 3 and C = Number of Columns = 2

df = (R-1) X ( C - 1)

df = (3-1)X (2-1)

df = 2 X 1

df = 2

[a] = 2

Part b) The critical chi-square value, beyond which 5% of the chi-square distribution lies (α=0.05) = [b].

Look in Chi-square table for df = 2 row and right tail area = 0.05 and find corresponding critical value.

Thus [b] = 5.99

Part c) Is there a significant association between race and LBW based on the α=0.05 test (does 8.20 exceed the critical value?). [c]

Chi-square calculated value=   exceed the critical value .

Thus we reject null hypothesis H0 and thus we conclude that there is a significant association between race and LBW.

Thus answer is: [c] = Yes.