Chapter 8: Sampling Methods and The Central Limit Theorem

Which of the following are true regarding parameters and statistics? Statistics are measures calculated from populations. Parameters are measures calculated from samples. U is a parameter in S squared is a statistic. o is a statistic and s is a parameter.

U is a parameter in S squared is a statistic.

Which of the following statements correctly describes the relationship between a population and a sample? Select all that apply. A sample is a subset of the population. A population is part of a sample. The sample statistic is probably not exactly the same as the corresponding population characteristic. Sample statistics are more accurate than population parameters. Samples are used to estimate population characteristics.

A sample is a subset of the population. The sample statistic is probably not exactly the same as the corresponding population characteristic. Samples are used to estimate population characteristics.

"Destructive testing" Destroys a sample in the course of measuring it. Which of the following are some examples of this process? Select all that apply. Asking voters how they will cast their ballots in the next election. Evaluating coffee for taste and aroma. We need cereal to be sure each box contains the advertised amount. Determining a tables maximum load capacity by increasing its load until it breaks.

Evaluating coffee for taste and aroma. Determining a tables maximum load capacity by increasing its load until it breaks.

If a researcher was studying semester loads of students, which of the following might represent strata that would be appropriate for stratified random sampling? Select all that apply. Grouping students by marital status. Grouping students by last name. Grouping students by hair color. Grouping students as employed and unemployed.

Grouping students by marital status. Grouping students as employed and unemployed.

Choose the statement that best describes sampling error. The difference between a sample statistic and its corresponding population parameter. The sample that is selected using a process that is not random. The sample statistic that is not correctly calculated.

The difference between a sample statistic and its corresponding population parameter.

There are two conditions under which we can assume the sample means follows a normal distribution. What are they? We know that the population is on uniformly distributed. We know that the population is normally distributed. We don't know the population distribution, but the sample size is 30 or larger. Our sample is small, but we know that the population distribution is highly skilled.

We know that the population is normally distributed. We don't know the population distribution, but the sample size is 30 or larger.

A marketing firm is pulling 60 students at a college using a stratified sample. If 2/3 of the students are women and 1/4 of the students are from out of state, how many out-of-state students should be polled? 40 45 20 15

15

Suppose that a particular brand of 5 inch candles has an average life of 27 hours with a standard deviation of six hours. If all possible samples of 4 candles were selected in the average life of the samples was determined, what would the mean of the distribution of the sample means be? 5 3 4 27

27

Suppose that a particular brand of 13 ML trash bags as an average weight limit (the amount the bag to hold before birth bursting) of 12 pounds with a standard deviation of 2 pounds. If all possible samples of 16 bags were selected and the average weight limit of the samples was determined, what would the standard deviation of the distribution of sample means be? 2 16 0.5 12

0.5

How is a table of random numbers used to select a random sample? Choose the steps that make up the process. Items from the population are assigned sequential numbers. Numbers are always chosen by starting in the upper left corner. Numbers are chosen systematically from the random number table. Items who's number corresponds to random numbers become the sample.

Items from the population are assigned sequential numbers. Numbers are chosen systematically from the random number table. Items who's number corresponds to random numbers become the sample.

In order to apply the central limit theorem, what a assumption must be made about the shape of the population distribution? No information about the populations shape is needed. It must be known that the population is skewed left or right. It must be assume that the population is bell shaped. It must be known that the population is bell shaped.

No information about the populations shape is needed.

In cluster sampling the clusters are chosen from the population using simple random sampling. What kind of sampling is used within the individual clusters? Convenience sampling Non-probability sampling Random sampling Judgment sampling

Random sampling

Identify the steps required in taking a systematic random sample. Select all that apply. Select a random starting point. So if a random number K. Divide the population size by the sample size to find K. Select the first K items from the population. Select every Kth member of the population from the starting point.

Select a random starting point. Divide the population size by the sample size to find K. Select every Kth member of the population from the starting point.

Which statement correctly describes the relationship between the mean of the sample means and the population mean? The meaning of the sample means is the same as the population mean if the population distribution is normal. The meaning of the symbol means equals the population mean. The mean of the sample means is smaller than the population mean. The mean of the sample means is equal to the population mean divided by the square root of the sample size.

The meaning of the symbol means equals the population mean.

Which one of the following must be true for the sampling distribution of the sample mean to be normally distributed? The sample size must be less than 30 if the shape of the population is not known. The sample size must be at least 30 of the population follow the normal distribution. There is no requirement on the sample size if the population is normally distributed.

There is no requirement on the sample size if the population is normally distributed.

Which of the following statements which describes valid reasons to use a sample instead of evaluating a much larger population? Select all that apply. Sampling is a random process, and therefore more accurate than measuring the whole population. Example can be chosen to validate a specific idea about the population. To contact the entire population would be time consuming. Contacting the whole population would be only marginally more accurate than a sample.

To contact the entire population would be time consuming. Contacting the whole population would be only marginally more accurate than a sample.

What is the primary reason for using cluster sampling? To keep from destroying items. To allow access for the entire population. To reduce cost of sampling. To reduce accuracy.

To reduce cost of sampling.

Other reasons besides cost and size may make it difficult or impossible to evaluate the entire population. Which of the following describe such reasons? Select all that apply. A large part of the population may be physically and inaccessible. The population may consist of differing sub populations. The population may be changing too fast to allow complete sampling.

A large part of the population may be physically and inaccessible. The population may be changing too fast to allow complete sampling.

Choose the statement that best defines the sampling distribution of the sample mean. A probability distribution of all possible sample means of a given sample size. A probability distribution showing the mean and standard deviation of the population. A distribution showing the variation in sample means resulting from different sample sizes.

A probability distribution of all possible sample means of a given sample size.

What is a simple random sample? Choose one. A random sample with fewer than 10 items included in the sample. The sample chosen so that the extreme observations are included. A sample selected so that each member of the population has the same likelihood of being included. A sample chosen in the easiest way possible for the researcher so that the data may be collected quickly.

A sample selected so that each member of the population has the same likelihood of being included.

Which one of the following describes a random process that could be used to create a simple random sample? Selecting items from the population in a manner that is most convenient for the researcher. Asking your friends to choose a sample for you. Assigning numbers to members of the population and drawing the numbers out of a hat.

Assigning numbers to members of the population and drawing the numbers out of a hat.

Which of the file following populations is a good candidate for systematic random sampling? Students at a high school, arranged in order of their birthday. A customer list ordered by sales volume. The Fortune 500 list of corporations. Companies listed on the New York Stock Exchange.

Companies listed on the New York Stock Exchange.

Which of the following distinguish systematic random sampling from the simple random sample ling? Select all that apply. Systematic random sampling uses only one random choice, instead of several. Simple random sampling is more prone to buy us. Systematic random sampling can be more efficient in some situations. Simple random sampling requires a fewer random numbers.

Systematic random sampling uses only one random choice, instead of several. Systematic random sampling can be more efficient in some situations.

Which one of the following scenarios is not representative of destructive nature of testing? Testing to see which chocolate milk is preferred. Testing a lightbulb to estimate how long that last. Testing a student to measure his ability to recall a commercial message. Testing a tire to measure it's tread life.

Testing a student to measure his ability to recall a commercial message.

Economics play a role in the sampling process. Which statements correctly describe this relationship? Select all that apply. There are economies of scale in using a very large sample. The cost of studying an entire population may be prohibited. Doubling sample size doubles accuracy and is worth the cost. Large samples cost more in increasing size gives them diminishing marginal returns in accuracy.

The cost of studying an entire population may be prohibited. Large samples cost more in increasing size gives them diminishing marginal returns in accuracy.

In using a random number table to select a simple random sample, where does randomness occur in the process? Select all that apply. The manner in which numbers are taken from the table. The assignment of numbers to the items in the population. The correlation of the numbers from the population with the numbers from the table. The table Itself is one source of randomness.

The manner in which numbers are taken from the table. The table Itself is one source of randomness.

The central limit theorem describes the sampling distribution of the sample mean. Which one of these statements is correct? If the population is skewed, left or right, the sampling distribution of the sample mean will be uniform. The sampling distribution of the sample mean is nearly normal. As the sample size decreases, the sampling distribution of the sample mean more closely approaches the normal distribution.

The sampling distribution of the sample mean is nearly normal.

Which of the following statements about the sampling distribution of the sample means is not correct? The distribution of the sample mean tends to follow a normal distribution. The sample means dispersion is less than the population dispersion. The standard deviation of the sample mean is the same as that of the population. The sample mean is equal to the population mean.

The standard deviation of the sample mean is the same as that of the population.

Take the statement that describes the formula for the standard error of the mean in ordinary language. The standard error is equal to the sample standard deviation divided by the square root of the sample size. The standard error is equal to the population standard deviation divided by the square root of the sample size. The standard error of the sample means equals the population standard deviation multiplied by the square of the sample size.

The standard error is equal to the population standard deviation divided by the square root of the sample size.

There are many reasons why it may be undesirable to sample the entire population. Which of the following is a reason that a modest size sample may be adequate? A large book biased sample may do more harm than a smaller unbiased sample. Very few problems require 100% accuracy. The population is highly varied, and a small sample may reflect only a part of it.

Very few problems require 100% accuracy.