STATISTICS FOR HEALTH MANAGEMENT DECISION MAKING

(1) “Sample space” refers to all the possible outcomes of a particular process. The two possible outcomes from the flip of a coin – heads or tails – are frequently called the “sample space” for this process. How many separate outcomes does the sample space of three flips of a coin include?
Select one:

a. 8
b. 32
c. 12
d. 4

(2) Here is a concept check for conditional probability. The following table shows an age-sex breakdown of U.S. physicians in a recent year as reported by the AMA. One can think of cell values as proportions of the total population of U.S. physicians. What is the probability that one randomly selected physician is female if she is less than 45 years old (up to 2 decimal points)?
Select one:

a. 0.22
b. 0.14
c. 0.32
d. 0.44

(3) ______________ is the probability that one screens negative, given that one does not have the disease. Which below fits this definition?
Select one:

a. Sensitivity
b. Positive Predictive Value (PPV)
c. Specificity
d. Negative Predictive Value (NPV)

(4) The chart below shows the counts of patients with different types of health plans (A, B, C or D) and sex (Female, Male) in a clinic. There are a total of 50 patients (33 Female, 17 Male). For example there are 9 female patients with plan type A, and 4 male patients with plan type A. What is the marginal probability that a patient has plan type C (up to 2 decimal points)?

Select one:

a. 0.24
b. 0.27
c. 0.26
d. 0.28

(5) Which statement below correctly states that the two events (flip of coin A and B) are independent?
Select one:

a. Given that coin B flipped a “head”, then the probability of coin A flipping a “head” is lower than the marginal probability of coin A flipping “head”.
b. None of the above
c. Given that coin B flipped a “head”, then the probability of coin A flipping a “head” is higher than the marginal probability of coin A flipping “head”.
d. Given that coin B flipped a “head”, then the probability of coin A flipping a “head” is simply equal to the marginal probability of coin A flipping “head”.

(6) The chart below shows the counts of patients with different types of health plans (A, B, C or D) and sex (Female, Male) in a clinic. There are a total of 50 patients (33 Female, 17 Male). For example there are 9 female patients with plan type A, and 4 male patients with plan type A. What is the joint probability that a patient is Female or patient has plan Type D (up to 2 decimal points)?

Select one:

a. 0.2
b. 0.44
c. 0.1
d. 0.76

(7) Two doctors work in a clinic. Both doctors test all patients for flu infection. Let Event A denote that the first doctor makes positive diagnosis of flu. Probability of Event A is 0.03. Let Event B denote that the second doctors makes a positive diagnosis of flu. Probability of Event B is 0.06. Probability that both doctors makes positive diagnosis of flu is 0.02. In other words, P(A and B)=0.02. Which of the statement below is correct?
Select one:

a. Event A is not independent of Event B
b. Probability of Event A is higher than the probability of Event B
c. Event A is independent of Event B
d. It is not possible to determine whether Event A is independent of Event B

(8) Hospital records indicate that 10% of patients are admitted for surgical treatment, 20% are admitted for obstetrics, and 5% receive both obstetrics and surgical treatment. If a new patient is admitted to the hospital, what is the probability that the patient will be admitted for surgery, obstetrics, or both?
Select one:

a. 0.05
b. 0.15
c. 0.25
d. 0.30

(9) Suppose in a population, the probability that an individual contracts a disease is .04. Assume that the probability of contracting the disease is independent across individuals in the population. We randomly sample 2 individuals from the population. What is the probability that exactly 1 of the 2 will contract the disease?
Select one:

a. 0.136
b. 0.0576
c. 0.0384
d. 0.0768

(10) Probability of any arrival at an emergency room being an emergency is 0.646. Assume that arrivals are independent. What is the probability of the next four arrivals’ being two emergencies and two nonemergencies in that order (up to three decimal points)?
Select one:

a. 0.174
b. 0.017
c. 0.005
d. 0.052

(11) Which one of these below is not a characteristic of the binomial random variable?
Select one:

a. Each of the n independent trials result in one of two possible outcomes
b. Probability of success remains the same from trial to trial
c. Each of the n independent trials could result in three or more possible outcomes
d. Outcome of one trial does not affect the outcome of any other

(11) A primary care center sees hundreds of patient annually. Over the past year, they have calculated that about 30% of the visits to the primary care center results in a referral to the specialty clinic. For the next 50 patients who will visit the primary care clinic next week, what is the probability that there will be at most 10 referrals to the specialty clinic (3 decimal points)?
Select one:

a. 0.039
b. 0.079
c. 0.961
d. 0.921

(12) If X is a random variable with a normal distribution, and has a population mean equal to 50 and a population variance of 25, what is the probability that X is greater than or equal to 45 (in 3 decimal points)?
Select one:

a. 0.841
b. 0.579
c. 0.421
d. 0.158

(13) If X is a random variable with a normal distribution, and has a population mean equal to 50 and a population standard deviation (SD) of 5, how many SDs from the mean is when X=65?
Select one:

a. 5
b. 0.5
c. 0.3
d. 3

(14) Which of the below is not a characteristic of a Poisson process?
Select one:

a. The number of occurrences in mutually exclusive time intervals is statistically independent
b. The probability of two or more occurrences is small relative to the probability of one occurrence
c. The number of occurrences in a given time interval has the same probability for all time intervals
d. The number of occurrences in mutually exclusive time intervals is statistically dependent

(15) In an emergency room, on average 2 patients in any one-hour period are transferred to the operation room for emergency surgery. What is the probability that at most 1 emergency room patient is transferred to emergency surgery in a one-hour period (in 3 decimal points)?
Select one:

a. 0.135
b. 0.406
c. 0.594
d. 0.271

(16) A primary care center sees hundreds of patient annually. Over the past year, they have calculated that about 30% of the visits to the primary care center results in a referral to the specialty clinic. For (17) the next 50 patients who will visit the primary care clinic next week, what is the probability that there will be more than 20 referrals to the specialty clinic (3 decimal points)?
Select one:

a. 0.037
b. 0.048
c. 0.952
d. 0.963

(18) In an emergency room, on average 2 patients in any one-hour period are transferred to the operation room for emergency surgery. What is the probability that more than 3 emergency room patients are transferred to emergency surgery in a one-hour period (in 3 decimal points)?
Select one:

a. 0.820
b. 0.857
c. 0.180
d. 0.143

(19) Which of the statements is correct about Normal Distribution?
Select one:

a. It is not possible to compare its mean to its median without further information
b. Its mean is greater than its median
c. Its mean is smaller than its median
d. Its mean is identical to its median

(20) A primary care center sees hundreds of patient annually. Over the past year, they have calculated that about 30% of the visits to the primary care center results in a referral to the specialty clinic. For the next 50 patients who will visit the primary care clinic next week, what is the probability that there will be exactly 15 referrals to the specialty clinic (3 decimal points)?
Select one:

a. 0.569
b. 0.431
c. 0.122
d. 0.878