N1 + n2 - 2

Applications of Biostatistics in Clinical Data1.The duration of time from first exposure to HIV infection to AIDS diagnosis is called the incubation period. The incubation periods of a random sample of 7 HIV infected individuals is given below (in years):12.010.59.56.313.512.57.2a)Calculate the sample mean.Mean = (12.0 + 9.5 + 13.5 + 7.2 + 10.5 + 6.3 + 12.5) / 7 = 10.21b)Calculate the sample medianSort: 6.3, 7.2, 9.5, 10.5, 12.0, 12.5, 13.5Median = (n + 1) / 2 = 8/2 = 4thvalueMedian = 10.5c)Calculate the sample standard deviation.SD = √∑(푋−푋푏푎푟)2푛−1Xbar = 10.21SD = √∑(12.0−10.21)2+(9.5−10.21)2+(13.5−10.21)2+(7.2−10.21)2+(10.5−10.21)2+(6.3−10.21)2+(12.5−10.21)27−1SD = 2.71d)If the number 6.3 above were changed to 1.5, what would happento the sample mean, median and standard deviation? State whether each would increase, decrease, or remain the same.Mean = (12.0 + 9.5 + 13.5 + 7.2 + 10.5 + 1.5+ 12.5) / 7 = 9.52Sort: 1.5, 7.2, 9.5, 10.5, 12.0, 12.5, 13.5Median = (n + 1) / 2 = 8/2 = 4thvalueMedian = 10.5SD = √∑(푋−푋푏푎푟)2푛−1
Xbar = 10.21SD = √∑(12.0−10.21)2+(9.5−10.21)2+(13.5−10.21)2+(7.2−10.21)2+(10.5−10.21)2+(1.5−10.21)2+(12.5−10.21)27−1SD = 4.17By changing 6.3 to 1.5, Mean decreases, Median remains same and SD increases.e)Suppose instead of 7 individuals, we had 14 individuals. (we added 7 more observations). 12.010.55.29.56.313.113.512.510.77.214.96.58.17.9Make a guess of whether the sample mean and sample standard deviation for the 14 observations would increase, decrease or remain the same compared to answer in part (d).Mean = (5.2+6.3+6.5+7.2+7.9+8.1+9.5+10.5+10.7+12.0+12.5+13.1+13.5+14.9)/14 = 8.88Sort:5.2, 6.3, 6.5, 7.2, 7.9, 8.1, 9.5, 10.5, 10.7, 12.0, 12.5, 13.1, 13.5, 14.9Median = (n + 1) / 2 = 15/2 = 7.5thvalue(i.e. between 7thand 8thvalue)Median = (9.5 + 10.5)/2 = 10SD = √∑(푋−푋푏푎푟)2푛−1SD = 3.22By changing number of observations to 14, Mean decreases, Median increasesand SD decreases.2.A study is conducted concerning the blood pressure of 60 year old women with glaucoma. In the study, 200 women are randomly selected and the sample meansystolic blood pressure is 140 mm Hg and the sample standard deviation is 25 mm Hg.a.Calculate a 95% confidence interval for the true mean systolic blood pressure among the population of 60 year old women with glaucoma.Answer:95%n = 200