Homework SourseA study prospectively examined whether sleepdisordered breat
A study prospectively examined whether sleep-disordered breathing was associated with an increased risk of death from any cause in a cohort of 6294 adults participating in the Sleep Heart Health Study. Study participants were classified into four groups depending on the extent of their sleepdisordered 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.
death
no death
476
2953
320
1477
165
562
86
255
1047
5247
Do the study findings give evidence of a significant relationship between the extent of sleep-disordered breathing and death?
a) Under the null hypothesis of no relationship, find the expected counts for each category.
b) Find the chi-square statistic value.
c) Find the degrees of freedom for the appropriate chi-square test. d) Find the range of the p-value.
| none | mild | moderate | severe | total | |
|---|---|---|---|---|---|
| death no death | 476 2953 | 320 1477 | 165 562 | 86 255 | 1047 5247 |
| total | 3429 | 1797 | 727 | 341 |
Solution
Set up null and alternate hypotheses as:
H0:There s no relationship between the extent of sleep-disordered breathing and death
Ha: There is association between them
Two tailed chi square tst
Prepare contingency table
The chi-square statistic is 57.9082. The p-value is < 0.00001. The result is significant at p < .05.
df = 3
| Results | ||||||
| None | Mild | Moderate | Severe | Row Totals | ||
| Death | 476 (570.41) [15.63] | 320 (298.93) [1.49] | 165 (120.94) [16.06] | 86 (56.72) [15.11] | 1047 | |
| No death | 2953 (2858.59) [3.12] | 1477 (1498.07) [0.30] | 562 (606.06) [3.20] | 255 (284.28) [3.01] | 5247 | |
| Column Totals | 3429 | 1797 | 727 | 341 | 6294 (Grand Total) |
