ga du ha 15 br 8. Depression A study published in the Archives of General Psychi

Question

ga du ha 15 br 8. Depression A study published in the Archives of General Psychiatry examined the impact of depres- sion on a patient's ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depres- sion, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? a) What kind of design was used to collect these data? b) Write appropriate hypotheses. c) Are the assumptions and conditions necessary for 42. inference satisfied? d) Test the hypothesis and state your conclusion. e) Explain in this context what your P-value means. D If your conclusion is actually incorrect, which type of error did you commit? g) Create a 95% CI. h) Interpret your interval. 1) Carefully explain what "95% confidence" means.

Explanation / Answer

a. In this example, we used random experiment to collect the data.

b. H0 : pdepresssed = pnon-depressed

Ha : pdepressed >  pnon-depressed

where pdepressed = percent of people died after 4 year who are depressed.

pnon-depressed = percent of people died after 4 year who are not depressed.

c. Assumptions are

so, al the assumptions are ok here.

d. here p^depressed = 26/89 = 0.292

p^non-depressed = 67/361= 0.1856

so pooled estimate p= ( 26 + 67)/ (89 + 361) = 0.2067

standard error of sampling se0 = sqrt [p(1-p) (1/n1 + 1/n2)] = sqrt [0.2067 * 0.7933 * (1/89 + 1/361)] = 0.0479

so Test statistic

Z = (pdepressed -  pnon-depressed)/se0 = (0.292 - 0.1856)/ 0.0479 = 2.22

here Z > Zcritical which is 1.96 so we can reject the null hypothesis.

(e) P - value = Pr (pdepressed > 0.292 ; 0.1856; 0.0479) that means that what is the probability that probability of people dying is greater than 0.292 when mean dying probability is 0.1856.

(f) If our conclusion is actually incorrect, we are committing type I error.

(g) 95 % CI = (pdepressed -  pnon-depressed) +- Z95% se0

= 0.1064 +- 1.96 * 0.0479

= (0.0125, 0.2003)

(h) We can interpret that there are 95 % probability that difference between proportion of depressed people dying and nondepressed people dying in next 4 years are in between 1.25% to 20%.

(i) The 95% confidence is meant above.

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