Question

There are 2 different questions, and the data table is below each question. Please answers them all

1. A drug test is administered to 10000 individuals as indicated in the contingency table below.

1. Determine the specificity, the sensitivity the PPV and NPV of the test.
2. Also give the prevalence of drug use in the population.
3. Would you trust a positive result for this test (meaning does this accurately indicate that you are a drug user?)
4. Would you trust a negative result? (does this accurately indicate that you do not use drugs?)
5. If an employer used this test to screen applicants for positions and only those with a negative test were allowed would you consider this to be fair?

	Uses Drug	Does not Use Drug	Total
Test +	198	196	394
Test -	2	9604	9606
Total	200	9800	10000

2. Refer to the table below “Undergraduate Grade Record by Student Characteristic” to answer this question

1. What is the probability that a graduating senior has grades mostly consisting of B’s or higher? Show and justify your calculation
2. What is the probability that a student selected at random has grades mostly B’s given they are in the age range 19-23?
3. Suppose that 65% of the students are in the age range 19-23. What is the probability that a students selected at random is both in this age range and has grades that are B’s and C’s. Justify your calculation
4. Honors Problem: Write down a probability distribution from this chart – state the random variable, it’s possible outcomes and give the probability associated with each outcome

Student characteristic			C's and D's or lower	B's and C's	Mostly B's	A's and B's	Mostly A's
Gender	Men		38.8%	16.6%	22.6%	9.6%	12.4%
	Women		29.4%	16.2%	26.2%	12.0%	16.2%
Class Level	Graduating Senior		15.8%	21.9%	34.5%	14.7%	13.0%
	All othe class levels		35.4%	15.8%	23.6%	10.5%	14.7%
Age	18 or younger		42.6%	14.7%	23.4%	9.4%	10.0%
	19-23		38.1%	19.0%	25.1%	9.4%	8.3%
	24-29		33.3%	16.9%	24.7%	10.3%	14.9%
	30-39		23.1%	13.2%	25.9%	14.8%	23.0%
	40 and older		20.1%	10.1%	22.0%	14.8%	33.0%

Answer 1

1.

(a)

Specificity of the test is given by

Sensitivity of the test is given by

PPV of the test is given by

NPV of the test is given by

(b)

Prevalence of drug is given by

(c)

Positive predictive value is only 0.5025381 which means 50.25% of the positive results shown by this test are actually positive. So, we cannot trust a positive result for this test.

(d)

Negative predictive value is only 0.9997918 which means 99.98% of the negative results shown by this test are actually negative. So, we can trust a negative result for this test.

(e)

Only those with a negative test were allowed. Specificity of the test is 98% i.e. higher enough. So, in this procedure 98% of people who do not use the drug are allowed for positions after screening. Thus this is fair enough.