Need help A study compares the effectiveness of washing the hands with soap and

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A study compares the effectiveness of washing the hands with soap and rubbing the hands with alcohol in hospitals. 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 below shows the descriptive statistics on the bacteria counts for the two groups. Complete parts a though c below. a. For hand rubbers, from an interval that contains at least 75% of the bacterial counts. (0, 148) b. For hand washers, from an interval that contains at least 75% of the bacterial counts. (0, 260) On the basis of the results from parts a and b make an inference about the effectiveness of the two hand-cleaning methods. Choose the more effective method below. A. Here rubbing is more effective than hand washing. B. Here washing is more effective than hand washing. C. Both methods are equally effective.

Explanation / Answer

here we use standard normal variate Z-value for finding the interval and

(a) here we want to find the value of z such that P(Z>z)=0.75

and correspondind value of z=0.6745 ( using ms-excel command (normsinv(0.75))

now 0.6745=(x-32)/58

or, x=32+0.6745*58=71.12 (next whole number is 72

so answer is (0, 72)

(b) similarly for this case

0.6745=(x-64)/98

or, x=64+0.6745*98=130.1 ( next whole numbe is 131)

so answer is (0,131)

(c) since bacterial count for hand rubbing is less than hand washing, so hand rubbing is more effective than washing

right choice is A.Hand rubbing is more effective than hand washing

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