2. Handwashing versus handrubbing The British Medical Journal published the resu

Question

2. Handwashing versus handrubbing The British Medical Journal published the results of a study to compare the effectiveness of handwashing with soap and handrubbing with alcohol. Health care workers who used handrubbing had a mean bacterial count of 35 per hand and with a standard deviation of 59. Health care workers who used handwashing had a mean bacterial count of 69 per hand with a standard deviation of 106. In a random sample of 50 health care workers, all using the same method of cleaning their hands, the mean bacterial count per hand, ž, is less than 30. Give your opinion on whether this sample of workers used handrubbing with alcohol or handwashing with soap. uci--F2017 Eco...oc A Homework2 (2).pdf doc

Explanation / Answer

When Handwashing is considered
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
mean ( u ) = 35
standard Deviation ( sd )= 59
sample size (n) = 50
P(X < 30) = (30-35)/59/ Sqrt ( 50 )
= -5/8.3439= -0.5992
= P ( Z <-0.5992) From Standard NOrmal Table
= 0.2745

When Handrubbing is considered
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
mean ( u ) = 69
standard Deviation ( sd )= 106
sample size (n) = 50
P(X < 30) = (30-69)/106/ Sqrt ( 50 )
= -39/14.9907= -2.6016
= P ( Z <-2.6016) From Standard NOrmal Table
= 0.0046
Probability 0.0046 <0.05, which is outlier and can n't be possibile

hence the decision is sample of workers used handwashing with soap

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