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In Exercises 21鈥24, use these results from the 鈥1-Panel-THC鈥 test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results; among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 4-1, which is included with the Chapter Problem.)

Testing for Marijuana: Use If one of the test subjects is randomly selected, find the probability that the subject did not use marijuana. Do you think that the result reflects the general population rate of subjects who do not use marijuana?

Short Answer

Expert verified

The probability of selecting a subject who did not use marijuana is equal to 0.593.

As the probability is high, it is improbable that the results happened by chance. Therefore, it can be used to represent the general population rate of people who do not use marijuana.

Step by step solution

01

Given information

The numbers of positive and negative drug test results of subjects are provided.


Use Marijuana

Did not Use Marijuana

Total

Subject Tested Positive


24(FP)

143

Subject Tested Negative

3(FN)


157

Total

300

The frequencies are categorized as true and false results.

02

Define the probability of an event

The probability of an event involves two counts; favorable to the event and the total possible counts of outcomes in the sample space.

Mathematically, it is stated as:

PA=NumberofoutcomesfavorabletoATotaloutcomes

03

Compute the subjects in each category

The table below shows the number of subjects that fall into each category:


Use Marijuana

Did not Use Marijuana

Total

Subject Tested Positive

119

24

143

Subject Tested Negative

3

154

157

Total

122

178

300

The total number of subjects is equal to 300.

Let E be the event of selecting a subject who did not use marijuana.

The number of subjects who did not use marijuana is:

FalsePositive+TrueNegative=24+154=178

04

 Step 4: Compute the probability

The probability of selecting a subject who did not use marijuana is given as:

PE=178300=0.593

Therefore,the probability of selecting a subject who did not use marijuana is equal to 0.593.

05

Describe the relevance of results for the general population

As the probability is approximately equal to 60%, which is quite high, the chances that the results appeared by chance in sampling are unlikely. Also, the sample size is 300, which is quite large.

Therefore, it can be said that the result actually reflects the general population rate of subjects who do not use marijuana.

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