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Question: Depression. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient's ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 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 inference satisfied?
d) Test the hypothesis and state your conclusion.
e) Explain in this context what your P-value means.
f) If your conclusion is actually incorrect, which type of error did you commit?
You throw darts at a board until you hit the center area. Your probability of hitting the center area is p = 0.17.
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a test for a certain disease is found to be 96 accurate meaning that it will correctly diagnose the disease in 96 out
The 99% confidence interval using a t-distribution is ( ), ( ). Round to one decimal place as needed
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Show by induction on r that S ≡ 0, then that V ≡ 0. (b) Un is the unbiased estimator of g(Q) with smallest variance. Hint: For an unbiased estimator T with symmetrization W, W = Un by part (a).
In the 1970s, computers (even minicomputers) were very expensive. Since no one had their own computer, people had to share. Compared to today, computers in the 1970s were slow, with limited memory and storage facilities.
Show that, if N and X, X1, X2, . . . are independent random variables, N ∈ Ge(α), and X ∈ Be(β), then Y = X1 + X2 + · · · + XN has a geometric distribution, and determine the parameter.
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