Question

Question # 1

Rothenberg et al. (2004) investigated the effectiveness of using the Hologic Sahara Sonometer, a portable device that measures bone mineral density (BMD) in the ankle, in predicting a fracture. They used a Hologic estimated bone mineral density value of

.57 as a cutoff. The results yielded the following data:

	Fracture Present (D)	No Fracture Present (~D)	Total
BMD = 0.57 (T)	217	667	884
BMD > 0.57 (~T)	70	333	403
Total	287	1000	1287

a. Compute the Sensitivity of the test. (6 points)

b. Compute the Specificity of the test. (6 points)

c. Compute the Positive Predictive Value (6 points)

Question # 2

According to the most recent Davenport student profile, 28% of students are male. Given a sample of 15 students:

a. Find the probability that none are male. (6 points)

b. Find the probability that 10 are male. (6 points)

c. Find the probability that at least six are male. (6 points)

Answer 1

Question # 1

(a)

Sensitivity is given by:

(b)

Specificity is given by:

(c)

Positive Predictive Value (PPV) is given by:

Question #2

(a)

Binomial Distribution

n = 15

p = 0.28

q = 1- p = 0.72

So,

Answer is:

0.0072

(b)

So,

Answer is:

0.0017

(c)

P(X6) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

So,

P(X6) = 1 - 0.7780

           = 0.2220

So,

Answer is:

0.2220