Download Chapter2 Example using Chebyshev`s Rule, page 67 part d) For any

Chapter2
Example using Chebyshev's Rule, page 67 part d)
For any number k greater than 1, at least (1 – 1/k2) of the measurements will fall within k SDs of the
mean.
In hospitals a study compared the effectiveness of washing hands with soap vs cleaning hands with
alcohol. One group of health care workers cleaned their hands with alcohol while a second group
washed their hands with soap. The bacterial count on the hands of each worker was recorded. The
table below shows the descriptive statistics on the bacteria counts for the 2 groups.
Use of alcohol
Use of soap and water
Mean
40
61
Standard Deviation
62
103
a) For those who used alcohol form an interval that contains about 95% of the bacterial counts
(Note: bacterial count cannot be less than 0)
We do not know the distribution so first find the value of k for a 95% (area) interval. That is,
1 – 1/k2 = .95. Finish solving for k here.
Now that you have k for this problem, and using 40 and 62 for mean and SD, respectively, find
x  k (s )
b) Repeat for those who washed their hands with soap.
Now find x  k (s ) for mean and SD of 61 and 103 respectively.
c) On the basis of your results in parts a) and b), make an inference about the effectiveness of the
two hand cleaning methods.