In a recent experiment one group of nurses was given bottles of epinephrine labe

Question

In a recent experiment one group of nurses was given bottles of epinephrine labeled with a concentration of "1 mg in 1 mL solution, " and another group of nurses was given bottles labeled with a ration of "1 mL of a 1: 1000 solution." Results are shown below about whether the dosage was correctly prepared or not. If one of the nurses is selected, what is the probability of getting one who calculated the dose incorrectly? If one of the nurses is selected, what is the probability of getting one who calculated the dose correctly? If one of the nurses is selected, what is the probability of getting one who made a correct dosage calculation or was given the bottle with a concentration label? If one of the nurses is selected what is the probability of getting one who made a wrong dosage calculation or was given the bottle with a ratio label? For the nurses given bottles labeled with a concentration, what is the percentage of correct dosage calculations? For the nurses given bottle labeled with a ratio, what is the percentage of correct dosage calculations? Which method of labeling would you recommend? Answer either "Concentration" or "Ratio."

Explanation / Answer

Here we have given the 2 by 2 contingency table.

First we complete the contingency table.

Now we have to find following probabilities.

2.01

Here we have to find P(getting one who calculated the dose incorrectly).

P(getting one who calculated the dose incorrectly) = (14+29) / 76 = 43/76 = 0.5658

2.02

Here we have to find P(getting one who calculated the dose correctly).

P(getting one who calculated the dose correctly) = (21+12) / 76 = 33/76 = 0.4342

2.03

Here we have to find P(getting one who made a correct dosage calculation or was given the bottle with a concentration label).

P(getting one who made a correct dosage calculation or was given the bottle with a concentration label) = P(getting one who made a correct dosage calculation) + P(was given the bottle with a concentration label) - P(getting one who made a correct dosage calculation and was given the bottle with a concentration label)

= 33/76 + 35/76 - 21/76 = 0.6184

2.04

Here we have to find P(getting one who made a wrong dosage calculation or was given the bottle with a ratio label).

P(getting one who made a wrong dosage calculation or was given the bottle with a ratio label) = P(getting one who made a wrong dosage calculation) + P(was given the bottle with a ratio label) - P(getting one who made a wrong dosage calculation and was given the bottle with a ratio label)

= 43/76 + 41/76 - 29/76 = 55/76 = 0.7237

correct dosage calculation wrong dosage calculation total concentration label 21 14 35 ratio label 12 29 41 total 33 43 76

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