Question

In: Statistics and Probability

A new cold medication was tested by giving 125 people the drug and 100 people a...

A new cold medication was tested by giving 125 people the drug and 100 people a placebo. A control group consisted of 115 people who were given no treatment. The number of people in each group who showed improvement is shown in the table below.

Cold Drug Placebo Control Total
Improvement 72 55 38 165
No Improvement 53 45 77 175
Total 125 100 115 340

a) What is the probability that a randomly selected person in the study either was given the placebo or was in the control group?

b) What is the probability that a randomly selected person either was given the drug or improved?

c) What is the probability that a randomly selected person was given the drug and improved?

d) What is the probability that a randomly selected person who improved was given the drug?

e) What is the probability that a randomly selected person who was given the drug improved?

f) Based on these data, does the drug appear to be effective?

Solutions

Expert Solution

a) What is the probability that a randomly selected person in the study either was given the placebo or was in the control group?

Answer : Pr(Was given the placebo or was in the control group) = (Total in placabo and total in control group)/Total population = (100 + 115)/340 = 0.6324

(b) probability that a randomly selected person either was given the drug or improved

= (Total given the drugs + total improved - total drugs and improved)/Total populatiion = (125 + 165 - 72)/340 = 0.6412

(c) probability that a randomly selected person was given the drug and improved

= Total given drug and improved/ Total population = 72/340 = 0.2118

(d) probability that a randomly selected person who improved was given the drug

= Total people who was improved and given the drug/Total who was improved = 72/165 = 0.4364

(e) probability that a randomly selected person who was given the drug improved

= Total people who improved given the drg/Total who was given the drug = 72/125 = 0.576

(f) Yes, as the data, seems the drug appear to be effective.

orchestra answered 1 year ago
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