Question 1

The standard error of an estimate is the standard deviation of the sampling distribution of the estimate.It measures how much estimates from different samples vary.

Accepted Answer

The standard error of an estimate indeed measures the standard deviation of the sampling distribution of the estimate, reflecting how much estimates from different samples can be expected to vary.

Question 2

The standard error of the estimate measures how much estimates vary from sample to sample.

Accepted Answer

The standard error of the estimate quantifies the variability or dispersion of sample estimates around the true population parameter, indicating how much sample estimates differ from one sample to another.

Question 3

Nontruthful responses is an example of a nonsampling error.

Accepted Answer

Nontruthful responses fall under the category of nonsampling errors because they are errors not related to the process of selecting a sample from the population but rather to inaccuracies in data collection, recording, or analysis that can occur even with a complete census of the population.

Question 4

An estimator is said to be biased if the mean of its sampling distribution is not equal to the value of the population parameter being estimated.

Accepted Answer

A biased estimator does not have a mean equal to the parameter it is estimating, indicating a systematic error in the estimation process.

Question 5

The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.

Accepted Answer

The mean of the sampling distribution of the mean is equal to the mean of the original population, as the sampling distribution represents the distribution of sample means from all possible samples of a given size from the population.

Question 6

The size of a sample can be selected by first determining the desired standard error and then using the formula  to calculate n.

Accepted Answer

The answer of The size of a sample can be...

Question 7

The central limit theorem (CLT)states that the sampling distribution of the mean is approximately normal,no matter what the distribution of the population,as long as the sample size is large enough.

Accepted Answer

The central limit theorem indeed states that the sampling distribution of the sample mean will approximate a normal distribution as the sample size becomes large, regardless of the population's distribution shape.

Question 8

A confidence interval is an interval calculated from the population data,where we strongly believe the true value of the population parameter lies.

Accepted Answer

A confidence interval is calculated from sample data, not population data, and it is used to estimate the range in which the true population parameter is likely to lie.

Question 9

If the sample size is greater than 30,the Central Limit Theorem (CLT)will always guarantee that the sampling distribution of the sample mean is approximately normal.

Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal if the sample size is sufficiently large, typically n > 30, but this is not a strict rule and depends on the underlying population distribution.

Question 10

Voluntary response bias occurs when the responses to questions do not reflect what the investigator had in mind.

Accepted Answer

Voluntary response bias occurs when individuals choose themselves whether to participate in a survey or study, potentially leading to a non-representative sample because those who volunteer might have different opinions or characteristics than the general population.

Question 11

An unbiased estimate is a point estimate such that the mean of its sampling distribution is equal to the true value of the population parameter being estimated.

Accepted Answer

An unbiased estimate means that the average of the estimates from many samples will exactly equal the true population parameter, indicating that the estimate is accurate on average.

Question 12

The sampling distribution of any point estimate (such as the sample mean or proportion)is the distribution of the point estimates we would obtain from all possible samples of a given size drawn from the population.

Accepted Answer

The sampling distribution of a point estimate refers to the distribution of that estimate across all possible samples of a given size from the population, showing how the estimate varies due to sampling variability.

Question 13

A sample in which the sampling units are chosen from the population by means of a random mechanism is a _____ sample.
A)probability
B)judgmental
C)convenience
D)voluntary response

Accepted Answer

A probability sample is one in which the sampling units are chosen from the population by means of a random mechanism, ensuring that every unit has a known and non-zero chance of being selected.

Question 14

The central limit theorem (CLT)says that as long as the sample size is reasonably large,there is about a 95% chance that the magnitude of the sampling error for the mean will be no more than two standard errors.

Accepted Answer

The central limit theorem implies that the sampling distribution of the sample mean will be approximately normally distributed for large sample sizes, and about 95% of the data falls within two standard deviations (standard errors) from the mean in a normal distribution.

Question 15

A judgmental sample is a sample in which the
A)sampling units are chosen using a random number table.
B)quality of sampling units judged before they are added to the sample.
C)sampling units are chosen according to the sampler's judgment.
D)sampling units condemn the sampling method used.

Accepted Answer

In a judgmental sample, the selection of sampling units is based on the judgment of the person conducting the research, rather than using random methods. This approach is often used when specific expertise or insights are needed to select the most appropriate or representative units for the study.

Question 16

It is customary to approximate the standard error of the sample mean  by substituting the sample standard deviation s for  in the formula: SE(  )=  .

Accepted Answer

The answer of It is customary to approximate the standard...

Question 17

When the sample size is greater than 5% of the population,the formula for the standard error of the mean should be modified with a finite population correction.

Accepted Answer

When the sample size is greater than 5% of the population, the standard error of the mean formula should be adjusted to include a finite population correction factor to account for the added precision gained by sampling a significant portion of the population.

Question 18

A sample of size 20 is selected at random from a population of size N.If the finite population correction factor is 0.9418,then N must be 169.

Accepted Answer

The finite population correction factor is calculated as sqrt((N-n)/(N-1)). Solving 0.9418 = sqrt((N-20)/(N-1)) gives N ≈ 169.

Question 19

The sampling distribution of the mean will have the same standard deviation as the original population from which the samples were drawn.

Accepted Answer

The standard deviation of the sampling distribution of the mean (often called the standard error) is typically smaller than the standard deviation of the original population, and it decreases as the sample size increases, according to the formula σ/√n, where σ is the population standard deviation and n is the sample size.

Question 20

Estimation is the process of inferring the value of an unknown population parameter using data from a random sample drawn from the population.

Accepted Answer

Estimation involves using sample data to make inferences about the unknown parameters of a population, such as the mean or proportion, which is a fundamental concept in statistics.

Quiz 7: Sampling and Sampling Distributions