As an alternative to hand washing, some hospitals allow health workers to rub their hands with an alcohol-based antiseptic. The British Medical Journal (Aug. 17, 2002) reported on a study to compare the effectiveness of washing the hands with soap and rubbing the hands with alcohol. One group of health care workers used hand rubbing, while a second group used hand washing to clean their hands. The bacterial count (number of colony-forming units) on the hand of each worker was recorded. The table gives descriptive statistics on bacteria counts for the two groups of health care workers. a. For hand rubbers, form an interval that contains at least 75%75% of the bacterial counts. (Note: The bacterial count cannot be less than 0 .) b. Repeat part a for hand washers. c. On the basis of your results in parts a and b, make an inference about the effectiveness of the two handcleaning methods.
As an alternative to hand washing, some hospitals allow health workers to rub their hands with an alcohol-based antiseptic. The British Medical Journal (Aug. 17, 2002) reported on a study to compare the effectiveness of washing the hands with soap and rubbing the hands with alcohol. One group of health care workers used hand rubbing, while a second group used hand washing to clean their hands. The bacterial count (number of colony-forming units) on the hand of each worker was recorded. The table gives
a. For hand rubbers, form an interval that contains at least 75%75% of the bacterial counts. (Note: The bacterial count cannot be less than 0 .)
b. Repeat part a for hand washers.
c. On the basis of your results in parts a and b, make an inference about the effectiveness of the two handcleaning methods.
If you are not sure about the shape of population distribution then, the Chebyshev’s inequality theorem helps us to determine how values fall with in the K standard deviation of the mean.
The Chebyshev’s inequality theorem states that, (1 - 1/k2) of the data values falls inside the k standard deviation of the mean.
i.e., interval = x̄ ± k*s
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