Susan’s Practice Exam 1

Public Health 6450

1.  Describe the difference between an observational study and an experiment.

2.  Do you want high or low bias in samples and experiments?

3.  Do you want high or low variability in samples and experiments?

4.  How do you reduce the bias in a sample or experiment?

5.  How do you reduce the variability in an experiment?

6.  How do you reduce the variability in a sample?

7.  Consider the probability distribution below.

X / -2.1 / -1.0 / 1.5 / 1.6 / 1.9 / 2.1
P(X) / 0.05 / 0.2 / 0.25 / 0.1 / 0.1

Find the following probabilities:

a)  P( X = 1.5 )

b)  P( X £ 1.5 )

c)  P( X 1.5)

d)  P( X £ -1.0 or X 1.9 )

e)  P( X -1.0 and X £ 1.9)

8.  Assume X ~ N ( μX = 5, σX = 2 ). Find the following probabilities:

a)  P( X £ 3)

b)  P( X 3)

c)  P (X 3)

9.  Assume X is a continuous random variable, distributed uniformly on the interval from 2 to 5. [ I.e., X ~ U(2,5) ]

a)  Sketch the density curve for X.

b)  Find P( X 4)

c)  Find P( 3 < X < 4)

13.  Given the table of probabilities below, answer the following questions.

Grade
Pass / Fail
Study 0-3 hours / 0.2 / 0.19
Study > 3 hours / 0.6

a)  What is the probability that you study > 3 hours and fail?

b)  Find P( pass)

c)  Find P( fail )

d)  Find P( study > 3 hours)

e)  Find P( study 0-3 hours)

f)  Find P( pass | study > 3 hours)

g)  Find P (pass | study 0-3 hours)

h)  Find P( study > 3 hours | fail )

14.  For each of the following situations, indicate whether a binomial distribution is a reasonable probability model for the random variable X. Give your reasons for each case.

a)  You observe the sex of the next 50 children born at a local hospital. X is the number of girls among them.

b)  A couple decides to continue having children until their first girl is born. X is the total number of children that the couple has.

15.  Suppose X ~ B( n = 15, p = 0.3). (I.e, X has a binomial distribution with n = 15 and p = 0.3). Find the following probabilities.

a)  P( X = 3 )

b)  P( X £ 4 )

c)  P( X < 6 )

d)  P( X ³ 2 )

e)  P( X > 8 )

16.  Suppose X ~ B( n = 1500, p = 0.12 )

a)  Find the mean of X

b)  Find the standard deviation of X

c)  Use the normal approximation to find P( X < 170 ).

17.  A cytological test was undertaken to screen women for cervical cancer. The cytological test has a sensitivity of 40.6% and a specificity of 98.5%. Suppose the prevalence of cervical cancer in the population is 15 per 1000 people. Given that a test comes back positive, what is the probability that, in fact, cancer is present?

18.  Tim wants an estimate of his monthly weight accurate to within 3 pounds with 95% confidence. Examination of Tim’s past data reveals that over relatively short periods of time, his weight measurements are approximately normal with s=3. How many measurements must he take in order to achieve this margin?

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