Q. 3 CD4 cells are carried in the blood as part of the human immune system. One
ID: 3066307 • Letter: Q
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Q. 3 CD4 cells are carried in the blood as part of the human immune system. One of the effects of the HIV virus is that these cells die. The count of CD4 cells is used in determining the onset of full-blown AIDS in a patient. The file cd4.csv in the Datasets folder on Avenue contains the CD4 cell count for 20 patients when they were put onto an experimental treatment and again after one year of use. a) State the appropriate hypotheses to see if the treatment significantly increased the CD4 count of HIV-positive patients. b) Conduct the appropriate hypothesis test and verify any assumptions that are needed. c) Give a point estimate and two-sided 99% confidence interval for the change in CDI count after one yearExplanation / Answer
a)from above
a)slope b1 =Sxy/SSx =1.035
test stat t=b1/std error =1.035/0.233 =4.4422
b) as confidence interval =b1 +tcritical *std error =0.5454 ; 1.5243
c)as test stat is greater then crtical value. hence we can reject null hypothesis and conclude that test is significant
therefore there is significant asccociation b/w baseline and follow-up CD4 counts
x y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) Yi' (Y-Yi')^2 2.12 2.47 1.36 2.63 3.20 2.884283 0.17163056 4.35 4.61 1.13 0.27 0.13 5.192022 0.33874917 3.39 5.26 0.01 1.36 -0.82 4.198556 1.1266639 2.51 3.02 0.61 1.15 1.70 3.287879 0.071759 4.04 6.36 0.57 5.14 -0.12 4.871215 2.21648097 5.10 5.93 3.28 3.37 1.85 5.968167 0.00145671 3.77 3.93 0.23 0.03 0.05 4.591803 0.43798276 3.35 4.09 0.00 0.00 0.00 4.157161 0.00451065 4.10 4.88 0.66 0.62 0.01 4.933307 0.00284159 3.35 3.81 0.00 0.08 0.21 4.157161 0.12052099 4.15 4.74 0.74 0.42 0.04 4.98505 0.06004929 3.56 3.29 0.07 0.64 0.43 4.374482 1.1761012 3.39 5.55 0.01 2.12 -1.02 4.198556 1.82640156 1.88 2.82 1.98 1.62 2.82 2.635917 0.03388666 2.56 4.23 0.53 0.02 -0.21 3.339622 0.7927735 2.96 3.23 0.11 0.74 0.98 3.753566 0.27412117 2.49 2.56 0.64 2.35 2.46 3.267181 0.50010566 3.03 4.31 0.07 0.05 -0.23 3.826006 0.23425015 2.66 4.37 0.39 0.08 -0.40 3.443108 0.85912926 3.00 2.40 0.08 2.87 1.85 3.79496 1.94591406 Total 65.76 81.86 12.48 25.57 12.92 12.1953288 mean 3.29 4.09 SSx Ssy SxyRelated Questions
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