Question 1

Which of the following is a parameter?
A) the sample mean
B) the sample standard deviation
C) the sample proportion
D) all of these
E) none of these

Accepted Answer

Parameters are numerical characteristics of a population, such as the population mean, population standard deviation, and population proportion. Choices A, B, and C all refer to sample statistics, not population parameters.

Question 2

The error of estimation is the difference between a statistic computed from a sample and the corresponding parameter computed from the population.

Accepted Answer

This is a correct definition of the error of estimation.

Question 3

The process of inferring the values of unknown population parameters from those of known sample statistics is called estimation.

Accepted Answer

This is true, estimation is the process of using sample statistics to make inferences about population parameters that are unknown.

Question 4

The type of sample statistic that is used to make inferences about a given type of population parameter is called:
A) the estimator of that parameter
B) the confidence level of that parameter
C) the confidence interval of that parameter
D) the point estimate of that parameter
E) the interval estimate of that parameter

Accepted Answer

An estimator is a rule or formula that tells us how to calculate an estimate of a given parameter based on sample data.

Question 5

Estimation is best defined as:
A) a process of inferring the values of unknown population parameters from those of known sample statistics
B) a process of inferring the values of unknown samples statistics from those of known population parameters
C) any procedure that views the parameter being estimated not as a constant, but, just like the estimator, as a random variable
D) a sampling procedure that matches each unit from population A with a "twin" from population B so that any sample observation about a unit in population A automatically yields an associated observation about a unit in population B
E) both a process of inferring the values of unknown samples statistics from those of known population parameters and any procedure that views the parameter being estimated not as a constant, but, just like the estimator, as a random variable

Accepted Answer

Estimation involves using known sample statistics to infer unknown population parameters.

Question 6

The concept of margin of error applies directly when estimating the population mean  , but is not applicable when estimating the population proportion p.

Accepted Answer

The concept of margin of error is applicable when estimating both the population mean and proportion.

Question 7

If the campaign manager of John Kerry is interested in estimating the proportion of registered voters who will support Kerry on November 2^nd, 2004, the sample proportion would be the appropriate point estimate.

Accepted Answer

The sample proportion would be the appropriate point estimate for estimating the proportion of registered voters who will support Kerry on November 2^nd, 2004.

Question 8

If a store manager has recently stated that she estimates the mean amount spent per customer per visit to be between $38.75 and $72.23, the numbers $38.75 and $72.23 are considered point estimates for the true population mean.

Accepted Answer

Point estimates are single values that are used to estimate a population parameter. Therefore, a range of values cannot be considered a point estimate.

Question 9

A sample statistic such that the mean of all its possible values differs from the population parameter the statistic seeks to estimate is a biased estimator.

Accepted Answer

A biased estimator is one that systematically overestimates or underestimates the population parameter it seeks to estimate. If the mean of the possible values of a statistic differs from the population parameter, then the estimator is biased.

Question 10

A point estimate of a population parameter will likely be different from the corresponding population value due to the fact that point estimates are subject to sampling error.

Accepted Answer

Point estimates are calculated from a sample of the population, not the entire population itself. Therefore, they are subject to the natural variability and randomness of the sample, which can cause them to differ from the true population parameter. This difference is known as sampling error.

Question 11

An unbiased estimator is:
A) any sample statistic used to approximate a population parameter
B) a sample statistic, which has an expected value equal to the value of the population parameter
C) a sample statistic whose value is usually less than the value of the population parameter
D) a sample statistic whose value is usually greater than the value of the population parameter
E) any estimator whose standard error is relatively small

Accepted Answer

An unbiased estimator is a sample statistic that has an expected value equal to the value of the population parameter being estimated. This means that, on average, the estimator will provide an accurate estimate of the population parameter. Option A is too broad and does not include the criterion of having an expected value equal to the population parameter. Option C and D are not correct as unbiased estimators do not have a tendency to be either greater or less than the population parameter; they are simply as accurate as possible. Option E is incorrect as the size of the standard error does not determine whether an estimator is unbiased or not.

Question 12

If a store manager is interested in estimating the mean amount spent per customer per visit at her store, the sample mean  would be the approximate point estimate.

Accepted Answer

The sample mean is an approximate point estimate for the population mean amount spent per customer per visit.

Question 13

A point estimate is an estimate of a population parameter, expressed as a single numerical value.

Accepted Answer

A point estimate is indeed an estimate of a population parameter expressed as a single numerical value.

Question 14

From a sample of 200 items, 12 items are defective. The point estimate of the population proportion defective will be:
A) 12
B) 0.06
C) 16.67
D) 0.12
E) 1.6

Accepted Answer

The point estimate of the population proportion defective is calculated by dividing the number of defective items by the total number of items in the sample, which is 12/200 = 0.06.

Question 15

A sample statistic such that the mean of all its possible values equals the population parameter the statistic seeks to estimate is an unbiased estimator.

Accepted Answer

An estimator is considered unbiased if the mean of all its possible values is equal to the population parameter it seeks to estimate.

Question 16

An estimator is unbiased if the mean of its sampling distribution is the population parameter being estimated.

Accepted Answer

If the mean of the sampling distribution of an estimator is equal to the true population parameter, then the estimator is unbiased.

Question 17

Increasing the sample size n will result in a point estimate that is closer to the true value of the population parameter.

Accepted Answer

The answer of Increasing the sample size n will result...

Question 18

Which of the following statements is correct?
A) A point estimate is an estimate of the range of a population parameter.
B) An interval estimate is an estimate of the range for a sample statistic.
C) A point estimate is a single value estimate of the value of a population parameter.
D) An interval estimate is an estimate of the value of a population parameter.
E) A point estimate is an estimate of the midpoint of the range for a sample statistic.

Accepted Answer

A point estimate is a single value estimate of the value of a population parameter. Option A is incorrect because a point estimate is a single value, not a range. Option B is incorrect because an interval estimate is a range, not a single value. Option D is incorrect because an interval estimate is an estimate of the range, not a single value. Option E is incorrect because a point estimate is a single value, not the midpoint of a range.

Question 19

The margin of error equals the sum of an estimator's squared bias plus its variance.

Accepted Answer

The margin of error is typically defined as a measure of the precision (or degree of uncertainty) of an estimator and is influenced by factors such as sample size and variability. It is not directly related to the bias or variance of an estimator, although these can impact the overall accuracy of the estimate. The formula for margin of error typically depends on the distributional assumptions and statistical method used to compute the estimate, and may involve factors such as the standard error or degrees of freedom.

Question 20

A point estimate is defined as:
A) the average of the sample values
B) the average of the population values
C) a single value that is the best estimate of an unknown population parameter
D) a single value that is the best estimate of an unknown sample statistic
E) a single value that is the best estimate of the upper range of a population parameter

Accepted Answer

A point estimate is a single value that is the best estimate of an unknown population parameter. It is usually calculated from a sample and used to infer something about the population. It is not the average of the sample or population values, nor is it the best estimate of an unknown sample statistic or the upper range of a population parameter.

Quiz 8: Large-Sample Estimation

Which of the following is a parameter?

The error of estimation is the difference between a statistic computed from a sample and the corresponding parameter computed from the population.

The process of inferring the values of unknown population parameters from those of known sample statistics is called estimation.

The type of sample statistic that is used to make inferences about a given type of population parameter is called:

Estimation is best defined as:

The concept of margin of error applies directly when estimating the population mean , but is not applicable when estimating the population proportion p.

If the campaign manager of John Kerry is interested in estimating the proportion of registered voters who will support Kerry on November 2nd, 2004, the sample proportion would be the appropriate point estimate.

If a store manager has recently stated that she estimates the mean amount spent per customer per visit to be between $38.75 and $72.23, the numbers $38.75 and $72.23 are considered point estimates for the true population mean.

A sample statistic such that the mean of all its possible values differs from the population parameter the statistic seeks to estimate is a biased estimator.

A point estimate of a population parameter will likely be different from the corresponding population value due to the fact that point estimates are subject to sampling error.

An unbiased estimator is:

If a store manager is interested in estimating the mean amount spent per customer per visit at her store, the sample mean would be the approximate point estimate.

A point estimate is an estimate of a population parameter, expressed as a single numerical value.

From a sample of 200 items, 12 items are defective. The point estimate of the population proportion defective will be:

A sample statistic such that the mean of all its possible values equals the population parameter the statistic seeks to estimate is an unbiased estimator.

An estimator is unbiased if the mean of its sampling distribution is the population parameter being estimated.

Increasing the sample size n will result in a point estimate that is closer to the true value of the population parameter.

Which of the following statements is correct?

The margin of error equals the sum of an estimator's squared bias plus its variance.

A point estimate is defined as:

If the campaign manager of John Kerry is interested in estimating the proportion of registered voters who will support Kerry on November 2^nd, 2004, the sample proportion would be the appropriate point estimate.