OPRE 6301 Test 1 Statistics and Data Analysis Questions
and Answers
Question 1
Which of the following best describes stratified random sampling?
A. Selecting every kth element from a population
B. Dividing the population into groups and randomly sampling within each group
C. Selecting clusters and sampling all elements within them
D. Making predictions based on sample statistics
Answer: B – Stratified random sampling
Rationale: This method ensures representation from each subgroup (stratum), improving
accuracy compared to simple random sampling.
Question 2
The probability of event A given event B has occurred is expressed as:
A. P(A ∩ B)
B. P(A) + P(B)
C. P(A|B) = P(A ∩ B) / P(B)
D. P(A|B) = P(B ∩ A) / P(A)
Answer: C – Conditional probability formula
Rationale: Conditional probability divides the joint probability by the probability of the
conditioning event.
Question 3
Which type of error occurs when survey participants fail to respond?
A. Sampling error
B. Nonresponse error
C. Measurement error
D. Coverage error
Answer: B – Nonresponse error
Rationale: This bias arises when certain groups are underrepresented due to lack of
participation.
,Question 4
The mean of a sample is considered a:
A. Parameter
B. Statistic
C. Population measure
D. Random variable
Answer: B – Statistic
Rationale: A statistic summarizes sample data, while a parameter describes the entire
population.
Question 5
Which distribution is appropriate for modeling the number of successes in a fixed number of
independent Bernoulli trials?
A. Normal distribution
B. Binomial distribution
C. Poisson distribution
D. Exponential distribution
Answer: B – Binomial distribution
Rationale: The binomial distribution applies when outcomes are binary (success/failure) across
repeated trials.
Question 6
If the probability of success is 0.2, what is the expected number of successes in 10 trials?
A. 1
B. 2
C. 4
D. 5
Answer: B – 2 successes
Rationale: Expected value = n × p = 10 × 0.2 = 2.
Question 7
Which of the following is NOT a measure of central tendency?
, A. Mean
B. Median
C. Mode
D. Variance
Answer: D – Variance
Rationale: Variance measures dispersion, not central tendency.
Question 8
The empirical rule states that for a normal distribution:
A. 68% of data lies within 1 standard deviation
B. 95% within 2 standard deviations
C. 99.7% within 3 standard deviations
D. All of the above
Answer: D – All of the above
Rationale: The empirical rule summarizes the spread of data in a normal distribution.
Question 9
Which sampling technique involves selecting every kth element after a random start?
A. Cluster sampling
B. Systematic sampling
C. Stratified sampling
D. Convenience sampling
Answer: B – Systematic sampling
Rationale: This method ensures evenly spaced selections across the population.
Question 10
In hypothesis testing, the probability of rejecting a true null hypothesis is called:
A. Type I error
B. Type II error
C. Power
D. Confidence level
Answer: A – Type I error
Rationale: Type I error occurs when the null hypothesis is incorrectly rejected.
, Question 11
Which of the following is a continuous random variable?
A. Number of defective items in a batch
B. Time taken to complete a task
C. Number of customers arriving in an hour
D. Number of heads in coin tosses
Answer: B – Time taken to complete a task
Rationale: Time is measured on a continuous scale, unlike counts which are discrete.
Question 12
The variance of a dataset is defined as:
A. Average of squared deviations from the mean
B. Square root of standard deviation
C. Difference between maximum and minimum values
D. Average of absolute deviations
Answer: A – Average of squared deviations
Rationale: Variance quantifies spread by squaring deviations from the mean.
Question 13
Which sampling method is most prone to bias?
A. Simple random sampling
B. Stratified sampling
C. Convenience sampling
D. Systematic sampling
Answer: C – Convenience sampling
Rationale: Convenience sampling lacks randomness and often misrepresents the population.
Question 14
The central limit theorem states that:
A. Sample means approximate a normal distribution as sample size increases
B. Population distributions become normal with large samples
and Answers
Question 1
Which of the following best describes stratified random sampling?
A. Selecting every kth element from a population
B. Dividing the population into groups and randomly sampling within each group
C. Selecting clusters and sampling all elements within them
D. Making predictions based on sample statistics
Answer: B – Stratified random sampling
Rationale: This method ensures representation from each subgroup (stratum), improving
accuracy compared to simple random sampling.
Question 2
The probability of event A given event B has occurred is expressed as:
A. P(A ∩ B)
B. P(A) + P(B)
C. P(A|B) = P(A ∩ B) / P(B)
D. P(A|B) = P(B ∩ A) / P(A)
Answer: C – Conditional probability formula
Rationale: Conditional probability divides the joint probability by the probability of the
conditioning event.
Question 3
Which type of error occurs when survey participants fail to respond?
A. Sampling error
B. Nonresponse error
C. Measurement error
D. Coverage error
Answer: B – Nonresponse error
Rationale: This bias arises when certain groups are underrepresented due to lack of
participation.
,Question 4
The mean of a sample is considered a:
A. Parameter
B. Statistic
C. Population measure
D. Random variable
Answer: B – Statistic
Rationale: A statistic summarizes sample data, while a parameter describes the entire
population.
Question 5
Which distribution is appropriate for modeling the number of successes in a fixed number of
independent Bernoulli trials?
A. Normal distribution
B. Binomial distribution
C. Poisson distribution
D. Exponential distribution
Answer: B – Binomial distribution
Rationale: The binomial distribution applies when outcomes are binary (success/failure) across
repeated trials.
Question 6
If the probability of success is 0.2, what is the expected number of successes in 10 trials?
A. 1
B. 2
C. 4
D. 5
Answer: B – 2 successes
Rationale: Expected value = n × p = 10 × 0.2 = 2.
Question 7
Which of the following is NOT a measure of central tendency?
, A. Mean
B. Median
C. Mode
D. Variance
Answer: D – Variance
Rationale: Variance measures dispersion, not central tendency.
Question 8
The empirical rule states that for a normal distribution:
A. 68% of data lies within 1 standard deviation
B. 95% within 2 standard deviations
C. 99.7% within 3 standard deviations
D. All of the above
Answer: D – All of the above
Rationale: The empirical rule summarizes the spread of data in a normal distribution.
Question 9
Which sampling technique involves selecting every kth element after a random start?
A. Cluster sampling
B. Systematic sampling
C. Stratified sampling
D. Convenience sampling
Answer: B – Systematic sampling
Rationale: This method ensures evenly spaced selections across the population.
Question 10
In hypothesis testing, the probability of rejecting a true null hypothesis is called:
A. Type I error
B. Type II error
C. Power
D. Confidence level
Answer: A – Type I error
Rationale: Type I error occurs when the null hypothesis is incorrectly rejected.
, Question 11
Which of the following is a continuous random variable?
A. Number of defective items in a batch
B. Time taken to complete a task
C. Number of customers arriving in an hour
D. Number of heads in coin tosses
Answer: B – Time taken to complete a task
Rationale: Time is measured on a continuous scale, unlike counts which are discrete.
Question 12
The variance of a dataset is defined as:
A. Average of squared deviations from the mean
B. Square root of standard deviation
C. Difference between maximum and minimum values
D. Average of absolute deviations
Answer: A – Average of squared deviations
Rationale: Variance quantifies spread by squaring deviations from the mean.
Question 13
Which sampling method is most prone to bias?
A. Simple random sampling
B. Stratified sampling
C. Convenience sampling
D. Systematic sampling
Answer: C – Convenience sampling
Rationale: Convenience sampling lacks randomness and often misrepresents the population.
Question 14
The central limit theorem states that:
A. Sample means approximate a normal distribution as sample size increases
B. Population distributions become normal with large samples
