CD4 cells are carried in the blood as part of the human immune system. One of th
ID: 3177550 • Letter: C
Question
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. In this study of the effectiveness of a new anti-viral drug on HIV, 20 HIV-positive patients had their CD4 counts recorded (“Baseline”) and then were put on a course of treatment with this drug. After using the drug for one year, their CD4 counts were again recorded (“OneYear”). The aim was to show that patients taking the drug had increased CD4 counts which is not generally seen in HIV-positive patients.
Baseline
OneYear
2.12
2.47
4.35
4.61
3.39
5.26
2.51
3.02
4.04
6.36
5.1
5.93
3.77
3.93
3.35
4.09
4.1
4.88
3.35
3.81
4.15
4.74
3.56
3.29
3.39
5.55
1.88
2.82
2.56
4.23
2.96
3.23
2.49
2.56
3.03
4.31
2.66
4.37
3.00
2.40
The standard error for the coefficient for the slope for the above is 0.233 and the critical value for testing model coefficients is 2.10 (18 df).
1What would be the observed value of the test statistic for testing the above?
2) What would be the 95% confidence interval for the above slope?
3) What conclusion do you draw concerning the association of baseline and follow-up CD4 counts?
Baseline
OneYear
2.12
2.47
4.35
4.61
3.39
5.26
2.51
3.02
4.04
6.36
5.1
5.93
3.77
3.93
3.35
4.09
4.1
4.88
3.35
3.81
4.15
4.74
3.56
3.29
3.39
5.55
1.88
2.82
2.56
4.23
2.96
3.23
2.49
2.56
3.03
4.31
2.66
4.37
3.00
2.40
Explanation / 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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