Question

A study prospectively examined whether sleep-disordered breathing was associated with an increased risk of death from any cause in a cohort of 6292 adults participating in the Sleep Heart Health Study. Study participants were classified into four groups depending on the extent of their sleep-disordered breathing (none, mild, moderate, or severe). The counts of deaths over the course of the study are reported for each group in the two-way table below.

	none	mild	moderate	severe	Total
Death	476	320	165	84	1045
No Death	2953	1477	562	255	5247
Total	3429	1797	727	339	6292

Do the study findings give evidence of a significant relationship between the extent of sleep-disordered breathing and death?

(a) What is the appropriate test to address this question?

2-proportion z test

t-test for linear regression

one-way ANOVA F test

chi-square test of independence

Under the null hypothesis of no relationship,
(b) the expected cell count that from the severe sleep-discorered breathing and death cell is  (round to 2 decimal places)

(c) the contribution to the test statistic that comes from the severe sleep-disordered breathing and death cell is  (round to 2 decimal places)

Answer 1

a)

chi-square test of independence

b)

expected cell count =(row total*column total)/grand total =(1045*339/6292)=56.30
c)

contribution to the test statistic =(84-56.30)²/56.30 =13.63