Question 1

When all the items in a population have an equal chance of being selected for a sample,the process is called __________________.

Accepted Answer

Random sampling is the process in which each item in a population has an equal chance of being selected for a sample. This type of sampling helps to reduce bias and increase the generalizability of findings from the sample to the population.

Question 2

The standard error of the mean will vary according to the size of the sample.As the sample size n gets larger,the variability of the sample means gets smaller.

Accepted Answer

This statement is true. As the sample size gets larger, the standard error of the mean decreases, indicating that the estimate of the population mean becomes more precise.

Question 3

When dividing a population into subgroups so that a random sample from each subgroup can be collected,what type of sampling is used?

Accepted Answer

Stratified random sampling involves dividing the population into subgroups based on certain characteristics (such as age or gender) and then randomly selecting samples from each subgroup. This ensures that each subgroup is represented in the sample and can increase the accuracy of the results. Therefore, stratified random sampling is the best choice for this scenario.

Question 4

Fish and game wardens estimate the average weight of the fish or game population by using creel checks and other devices.Based on this sample data,a warden might estimate that the mean weight of Coho salmon caught in Lake Michigan is 2.5 pounds.This single number is called a point estimate of the unknown population parameter.

Accepted Answer

A point estimate is a single number used to estimate an unknown population parameter based on a sample of data. In this case, the fish and game warden used creel checks and other devices to estimate the average weight of Coho salmon caught in Lake Michigan, and the result was 2.5 pounds. Therefore, the statement is true.

Question 5

If the sample size keeps getting larger and larger and finally equals the size of the population,there would be no error in predicting the population mean because the sample size and the size of the population would be the same.

Accepted Answer

When the sample size equals the size of the population, it is called a census. In this case, the sample represents the entire population and there would be no sampling error in predicting the population mean. However, there may still be other sources of error, such as measurement error or response bias.

Question 6

If 40 samples of size 21 were selected from a population of 22,493,we would expect the mean of the sample means and the population mean to be close but not exactly equal.

Accepted Answer

This is because the sample means would follow a normal distribution with a mean equal to the population mean and a standard error of the population standard deviation divided by the square root of the sample size. As the number of samples increases, the distribution of sample means becomes more and more concentrated around the population mean, but it will never be exactly equal due to the variability in the sampling process.

Question 7

Based on the central limit theorem,sampling error will decrease as sample size increases.

Accepted Answer

The central limit theorem states that as sample size increases, the distribution of sample means will approach a normal distribution and have a smaller standard error. This means that sampling error, which is the difference between the sample mean and the population mean, will decrease as sample size increases. Therefore, the statement is true.

Question 8

Based on the sampling distribution of the means and the central limit theorem,the sample mean can be used as a good estimator of the population mean,assuming that the size of the sample is sufficiently large.

Accepted Answer

The central limit theorem states that as the sample size increases, the distribution of sample means approaches a normal distribution regardless of the distribution of the population. This means that the sample mean can be a good estimator of the population mean, as long as the sample size is sufficiently large.

Question 9

Suppose we select every fifth invoice in a file.What type of sampling is this?

Accepted Answer

This is systematic sampling where every fifth invoice is selected based on a predetermined pattern or interval.

Question 10

All possible samples of size n are selected from a population and the mean of each sample is determined.What is the mean of the sample means?

Accepted Answer

The mean of the sample means is known as the sample mean or the expected value of the sample means. By the Law of Large Numbers, as the sample size increases, the sample mean will approach the population mean. Therefore, the mean of the sample means is exactly the same as the population mean.

Question 11

The mean of all possible sample means is equal to the population mean.

Accepted Answer

This statement is true and is central to the concept of the central limit theorem, which states that as sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the population mean.

Question 12

The Central Limit Theorem states that for a sufficiently large sample the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed with the mean of the sampling distribution equal to µ and the variance equal to $\sigma$²/n.

Accepted Answer

The statement accurately describes the Central Limit Theorem.

Question 13

An estimate of the population mean based on a large sample is less reliable than an estimate made using a small sample.

Accepted Answer

This statement is false. A larger sample size generally leads to a more accurate estimate of the population mean, as the larger sample size reduces the effect of random sampling error.

Question 14

The Central Limit Theorem states that for a sufficiently large sample the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed with the mean of the sampling distribution equal to $\sigma$²and the variance equal to $\sigma$^2/ⁿ.

Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed with the mean equal to the population mean (μ) and the variance equal to the population variance (σ²) divided by the sample size (n).

Question 15

To determine the value of the standard error of the mean,the total error is divided by the sample size.

Accepted Answer

The answer of To determine the value of the standard...

Question 16

The Central Limit Theorem states that if the sample size,n,is sufficiently large,the sampling distribution of the means will be approximately normal no matter whether the population is normally distributed,skewed,or uniform.

Accepted Answer

The statement accurately represents the Central Limit Theorem.

Question 17

What sample statistic is used to estimate a population parameter?

Accepted Answer

A point estimate is a single value that is used to estimate the value of a population parameter. It is calculated from a sample statistic, such as the sample mean or sample proportion.

Question 18

Based on the central limit theorem,sampling error will decrease as sample size decreases.

Accepted Answer

According to the central limit theorem, sampling error decreases as sample size increases, not decreases. This is because as sample size increases, the sample mean becomes more representative of the population mean, reducing the chance of random error in the sample.

Question 19

The true sampling error is usually not known because

Accepted Answer

The true sampling error is not known because the population mean (µ) is unknown.

Question 20

What is the difference between a sample mean and the population mean called?

Accepted Answer

Sampling error is the difference between a sample statistic (such as sample mean) and the corresponding population parameter (such as population mean). This error arises because the sample is not a perfect representation of the population.

Quiz 8: Sampling Methods and the Central Limit Theorem