Fundamentals of Biostatistics 8th Edition Rosner Solutions Manual
Complete Solution Manual Fundamentals of Biostatistics 8th Edition Rosner Questions & Answers with rationales
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s = standard deviation = variance = 5.72 days
range = largest − smallest observation = 30 − 3 = 27 days
20.3 Suppose we divide the patients according to whether or not they received antibiotics, and calculate the
mean and standard deviation for each of the two subsamples:
x s n
Antibiotics 11.57 8.81 7
No antibiotics 7.44 3.70 18
Antibiotics - x7 8.50 3.73 6
It appears that antibiotic users stay longer in the hospital. Note that when we remove observation 7, the
two standard deviations are in substantial agreement, and the difference in the means is not that
impressive anymore. This example shows that x and s2 are not robust; that is, their values are easily
affected by outliers, particularly in small samples. Therefore, we would not conclude that hospital stay is
different for antibiotic users vs. non-antibiotic users.
2
,CHAPTER 2/DESCRIPTIVE STATISTICS 3
2.4-2.7 Changing the scale by a factor c will multiply each data value xi by c, changing it to cxi . Again the same
individual’s value will be at the median and the same individual’s value will be at the mode, but these
values will be multiplied by c. The geometric mean will be multiplied by c also, as can easily be shown:
Geometric mean = [(cx1)(cx2 ) (cxn )]1/n
= (cn x1 x2 xn )1/n
= c( x1 x2 xn )1/n
= c old geometric mean
The range will also be multiplied by c.
For example, if c = 2 we have:
xi
Original Scale
–3 –2 –1 0 1 2 3
xi
Scale 2
–6 –4 –2 0 2 4 6
2.8 We first read the data file “running time” in R
> require(xlsx)
> running<-na.omit(read.xlsx("C:/Data_sets/running_time.xlsx",1,
header=TRUE))
Let us print the first observations
> head(running)
week time
1 1 12.80
2 2 12.20
3 3 12.25
4 4 12.18
5 5 11.53
6 6 12.47
The mean 1-mile running time over 18 weeks is equal to 12.09 minutes:
> mean(running$time)
[1] 12.08889
2.9 The standard deviation is given by
> sd(running$time)
[1] 0.3874181
2.10 Let us first create the variable “time_100” and then calculate its mean and standard deviation
> running$time_100=100*running$time
> mean(running$time_100)
[1] 1208.889
> sd(running$time_100)
[1] 38.74181
2.11 Let us to construct the stem-and-leaf plot in R using the stem.leaf command from the package “aplpack”
> require(aplpack)
Note: one can also use the standard command stem (which does require the “aplpack” package) to get a similar plot
> stem(running$time_100, scale = 4)
Box plot of running times
2.15 We provide two rows for each stem corresponding to leaves 5-9 and 0-4 respectively. We have
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