OPRE 6301 – 7 EXAM QUESTIONS AND
ANSWERS 2026 VERIFIED.
If two random samples of sizes 30 and 36 are selected independently from two populations
with means 78 and 85, and standard deviations 12 and 15, respectively, then the mean of the
difference xbar1 - xbar2 is equal to:
−7
7
(78 − 85) / (30 − 36) = 1.17
78/30 − 85/36 = 0.24 - ANS -7
Given a binomial distribution with n trials and probability p of a success on any trial, a
conventional rule of thumb is that the normal distribution will provide an adequate
approximation of the binomial distribution if
np ≥ 5 and n(1 − p) ≥ 5
np ≥ 5 and np(1 − p) ≥ 5
np ≤ 5 and n(1 − p) ≤ 5
None of these choices. - ANS np ≥ 5 and n(1 − p) ≥ 5
A sample of size 200 is taken at random from an infinite population. Given that the population
proportion is 0.60, the probability that the sample proportion is less than 0.58 is
@2026/2027 ALLRIGHTS RESERVED.
,0.281
0.719
0.580
0.762 - ANS 0.281
The standard error of the sample proportion gets larger as:
Selected
p approaches 0
p approaches 0.50
p approaches 1.00
None of these choices. - ANS p approaches 0.50
Recall the rule of thumb used to indicate when the normal distribution is a good approximation
of the sampling distribution for the sample proportion p hat. For the combination n = 50, p =
0.05, the rule is satisfied. - ANS False
If a simple random sample of 300 observations is taken from a population whose proportion p =
0.6, then the expected value of the sample proportion is 0.60. - ANS True
Which of the following is a characteristic for a good estimator?
Being unbiased
Being consistent
Having relative efficiency
All of these choices are true. - ANS All of these choices are true.
@2026/2027 ALLRIGHTS RESERVED.
, A point estimator is defined as:
a range of values that estimates an unknown population parameter.
a range of values that estimates an unknown sample statistic.
a single value that estimates an unknown population parameter.
a single value that estimates an unknown sample statistic. - ANS a single value that estimates
an unknown population parameter.
An unbiased estimator of a population parameter is defined as:
an estimator whose expected value is equal to the parameter.
an estimator whose variance is equal to one.
an estimator whose expected value is equal to zero.
an estimator whose variance goes to zero as the sample size goes to infinity. - ANS an
estimator whose expected value is equal to the parameter.
An estimator is said to be consistent if:
it is an unbiased estimator.
the variance of the estimator is zero.
the difference between the estimator and the population parameter stays the same as the
sample size grows larger.
the difference between the estimator and the population parameter grows smaller as the
sample size grows larger. - ANS the difference between the estimator and the population
parameter grows smaller as the sample size grows larger.
@2026/2027 ALLRIGHTS RESERVED.
ANSWERS 2026 VERIFIED.
If two random samples of sizes 30 and 36 are selected independently from two populations
with means 78 and 85, and standard deviations 12 and 15, respectively, then the mean of the
difference xbar1 - xbar2 is equal to:
−7
7
(78 − 85) / (30 − 36) = 1.17
78/30 − 85/36 = 0.24 - ANS -7
Given a binomial distribution with n trials and probability p of a success on any trial, a
conventional rule of thumb is that the normal distribution will provide an adequate
approximation of the binomial distribution if
np ≥ 5 and n(1 − p) ≥ 5
np ≥ 5 and np(1 − p) ≥ 5
np ≤ 5 and n(1 − p) ≤ 5
None of these choices. - ANS np ≥ 5 and n(1 − p) ≥ 5
A sample of size 200 is taken at random from an infinite population. Given that the population
proportion is 0.60, the probability that the sample proportion is less than 0.58 is
@2026/2027 ALLRIGHTS RESERVED.
,0.281
0.719
0.580
0.762 - ANS 0.281
The standard error of the sample proportion gets larger as:
Selected
p approaches 0
p approaches 0.50
p approaches 1.00
None of these choices. - ANS p approaches 0.50
Recall the rule of thumb used to indicate when the normal distribution is a good approximation
of the sampling distribution for the sample proportion p hat. For the combination n = 50, p =
0.05, the rule is satisfied. - ANS False
If a simple random sample of 300 observations is taken from a population whose proportion p =
0.6, then the expected value of the sample proportion is 0.60. - ANS True
Which of the following is a characteristic for a good estimator?
Being unbiased
Being consistent
Having relative efficiency
All of these choices are true. - ANS All of these choices are true.
@2026/2027 ALLRIGHTS RESERVED.
, A point estimator is defined as:
a range of values that estimates an unknown population parameter.
a range of values that estimates an unknown sample statistic.
a single value that estimates an unknown population parameter.
a single value that estimates an unknown sample statistic. - ANS a single value that estimates
an unknown population parameter.
An unbiased estimator of a population parameter is defined as:
an estimator whose expected value is equal to the parameter.
an estimator whose variance is equal to one.
an estimator whose expected value is equal to zero.
an estimator whose variance goes to zero as the sample size goes to infinity. - ANS an
estimator whose expected value is equal to the parameter.
An estimator is said to be consistent if:
it is an unbiased estimator.
the variance of the estimator is zero.
the difference between the estimator and the population parameter stays the same as the
sample size grows larger.
the difference between the estimator and the population parameter grows smaller as the
sample size grows larger. - ANS the difference between the estimator and the population
parameter grows smaller as the sample size grows larger.
@2026/2027 ALLRIGHTS RESERVED.
