Chapter 6 – Point Estimation
COMPLETION
1. The objective of is to select a single number such as , based on sample data, that represents
a sensible value (good guess) for the true value of the population parameter, such as .
ANS: point estimation
PTS: 1
2. Given four observed values: would result in a point estimate for that
is equal to .
ANS: 5
PTS: 1
3. An estimator that has the properties of and will often be regarded as an accurate estimator.
ANS: unbiasedness, minimum variance
PTS: 1
4. A point estimator is said to be an estimator of if for every possible value of .
ANS: unbiased
PTS: 1
5. The sample median and any trimmed mean are unbiased estimators of the population mean if the random
sample from a population that is and .
ANS: continuous, symmetric
PTS: 1
6. Among all estimators of parameter that are unbiased, choose the one that has minimum variance. The resulting
is called the of .
ANS: minimum variance unbiased estimator (MVUE)
PTS: 1
7. The standard error of an estimator is the of .
ANS: standard deviation
PTS: 1
, 8. In your text, two important methods were discussed for obtaining point estimates: the method of and the
method of .
ANS: moments, maximum likelihood
PTS: 1
9. Let be a random sample from a probability mass function or probability density function f(x). For
k = 1,2,3,……, the kth population moment is denoted by , while the kth sample moment is .
ANS:
PTS: 1
10. Let be a random sample of size n from an exponential distribution with parameter . The moment
estimator of = .
, ANS:
PTS: 1
11. Let be the maximum likelihood estimates (mle’s) of the parameters . Then the mle of
any function h( ) of these parameters is the function of the mle’s. This result is known
as the principle.
ANS: invariance
PTS: 1
MULTIPLE CHOICE
1. Which of the following statements are true?
a. A point estimate of a population parameter is a single number that can be regarded as a sensible
value of .
b. A point estimate of a population parameter is obtained by selecting a suitable statistic and
computing its value from the given sample data. The selected statistic is called the point estimator
of .
c. The sample mean is a point estimator of the population mean .
d. The sample variance is a point estimator of the population variance .
e. All of the above statements are true.
ANS: E PTS: 1
2. Which of the following statements are not true?
a.
The symbol is customarily used to denote the estimator of parameter and the point estimate
resulting from a given sample.
b. The equality is read as “the point estimator of
c. The difference between and the parameter is referred to as error of estimation.
d. None of the above statements is true.
ANS: B PTS: 1
3. Which of the following statements are not always true?
a.
A point estimator is said to be an unbiased estimator of parameter if for every possible
b. value of .
If the estimator is not unbiased of parameter , the difference is called the bias of .
c. A point estimator is unbiased if its probability sampling distribution is always “centered” at the
true value of the parameter , where “centered” here means that the median of the distribution of
.
d. All of the above statements are true.
ANS: C PTS: 1
4. Which of the following statements are not always true?
COMPLETION
1. The objective of is to select a single number such as , based on sample data, that represents
a sensible value (good guess) for the true value of the population parameter, such as .
ANS: point estimation
PTS: 1
2. Given four observed values: would result in a point estimate for that
is equal to .
ANS: 5
PTS: 1
3. An estimator that has the properties of and will often be regarded as an accurate estimator.
ANS: unbiasedness, minimum variance
PTS: 1
4. A point estimator is said to be an estimator of if for every possible value of .
ANS: unbiased
PTS: 1
5. The sample median and any trimmed mean are unbiased estimators of the population mean if the random
sample from a population that is and .
ANS: continuous, symmetric
PTS: 1
6. Among all estimators of parameter that are unbiased, choose the one that has minimum variance. The resulting
is called the of .
ANS: minimum variance unbiased estimator (MVUE)
PTS: 1
7. The standard error of an estimator is the of .
ANS: standard deviation
PTS: 1
, 8. In your text, two important methods were discussed for obtaining point estimates: the method of and the
method of .
ANS: moments, maximum likelihood
PTS: 1
9. Let be a random sample from a probability mass function or probability density function f(x). For
k = 1,2,3,……, the kth population moment is denoted by , while the kth sample moment is .
ANS:
PTS: 1
10. Let be a random sample of size n from an exponential distribution with parameter . The moment
estimator of = .
, ANS:
PTS: 1
11. Let be the maximum likelihood estimates (mle’s) of the parameters . Then the mle of
any function h( ) of these parameters is the function of the mle’s. This result is known
as the principle.
ANS: invariance
PTS: 1
MULTIPLE CHOICE
1. Which of the following statements are true?
a. A point estimate of a population parameter is a single number that can be regarded as a sensible
value of .
b. A point estimate of a population parameter is obtained by selecting a suitable statistic and
computing its value from the given sample data. The selected statistic is called the point estimator
of .
c. The sample mean is a point estimator of the population mean .
d. The sample variance is a point estimator of the population variance .
e. All of the above statements are true.
ANS: E PTS: 1
2. Which of the following statements are not true?
a.
The symbol is customarily used to denote the estimator of parameter and the point estimate
resulting from a given sample.
b. The equality is read as “the point estimator of
c. The difference between and the parameter is referred to as error of estimation.
d. None of the above statements is true.
ANS: B PTS: 1
3. Which of the following statements are not always true?
a.
A point estimator is said to be an unbiased estimator of parameter if for every possible
b. value of .
If the estimator is not unbiased of parameter , the difference is called the bias of .
c. A point estimator is unbiased if its probability sampling distribution is always “centered” at the
true value of the parameter , where “centered” here means that the median of the distribution of
.
d. All of the above statements are true.
ANS: C PTS: 1
4. Which of the following statements are not always true?
