Chapter 8: Sampling, Sampling Methods, and the Central Limit Theorem - SmartBook

The average height of American women (in 2016) is 5 ft. 4 inches (64 inches) with a standard deviation of 3 inches. What is the probability that the average height of a random group of nine American women would be less than five feet three inches? Assume that the heights of American women are normally distributed.

0.1587

The average height of American males (in 2016) is 5 ft. 9 1/2 inches (69.5 inches) with a standard deviation of 3 inches. What is the probability that the average height of a random group of 16 American men would be over five feet ten inches? Assume that the heights of American men are normally distributed.

0.2514

A marketing firm is polling 60 students at a college using a stratified sample. If two thirds of the students are women, and one quarter of the students are from out of state, how many out-of-state students should be polled?

15

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.

Which of the following meet the conditions under which a sample mean will follow a normal distribution?

A sample of 20 is taken from a normally distributed population A sample size of 50 is taken from a population whose distribution is unknown

What is a simple random sample? Choose one.

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

Which one of the following statements is true about the dispersion of the distribution of sample means?

As the sample size increases, the variability in the sample means decreases.

Which of the following populations is a good candidate for Systematic random sampling?

Companies listed on the New York Stock Exchange.

Which of the following statements describe valid reasons to use a sample instead of evaluating a much larger population? Select all that apply.

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

Identify the steps that are followed in taking a stratified random sample. Select all that apply.

Measure the size of the strata as a proportion of the population. Determine what portion of the sample should come from each strata. Take random samples from each strata.

Which of the following are methods of obtaining a simple random sample from the population of all students at a particular college? Select all that apply.

Drawing 100 student names from a box. Using computer software to select 100 students. Using a random number table to select 100 students.

"Destructive Testing" destroys a sample in the course of measuring it. Which of the following are examples of this process? Select all that apply.

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

Which of the following statements are true features of the Central Limit Theorem? Select all that apply.

For large sample size, the distribution of sample means is independent of the shape of the population. The distribution shape is approximately Normal. It describes the sampling distribution of the sample mean.

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 as employed and unemployed. Grouping students by marital status.

Choose the two statements that are correct descriptions of the sampling distribution of the sample mean.

It is a distribution of means from samples of all one size. It is a probability distribution of all possible sample means.

"Destructive Testing" destroys a sample in the course of measuring it. Which of the following are examples of this process? Select all that apply.

Product testing for a new flavor of Coke. Measuring the cholesterol content of eggs.

In cluster sampling the clusters are chosen from the population using simple random sampling. What kind of sampling is used within the individual clusters?

Random sampling Reason: When sampling is used, it is done randomly. Sometimes a census is taken of selected clusters.

Which of the following statements correctly describe the relationship between a population and a sample? Select all that apply.

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

Identify the steps involved in taking a cluster sample. Select all that apply.

Select a random sample from each sub group. Divide the population into groups using naturally occurring boundaries. Randomly select a subset of clusters.

Identify the steps required in taking a systematic random sample. Select all that apply.

Select a random starting point. Select every kth member of the population from the starting point.

What characterizes a "strata" within a population?

Some identifiable characteristic that clearly divides the population into groups.

Why is systematic random sampling sometimes used in place of simple random sampling?

Sometimes it is difficult to assign random numbers.

There are many reasons why it may be undesirable to sample an entire population. Which of the following is a reason that a modest size sample may be adequate?

Very few problems require 100% accuracy.

Which of the following distinguish systematic random sampling from simple random sampling? Select all that apply.

Systematic random sampling uses only one random choice, instead of several. Systematic random sampling is quicker and easier.

What is a simple random sample? Choose one.

Ten cities in Illinois are randomly selected using a random number list.

Economics plays a role in the sampling process. Which statements correctly describe this relationship? Select all that apply.

The cost of studying an entire population may be prohibitive. Larger samples cost more, and increasing size gives diminishing marginal returns in accuracy.

Choose the statement that best describes sampling error.

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

What characteristic of a population makes it a good candidate for cluster sampling?

The population is widely scattered over a large geographical area.

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

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

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.

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

The Central Limit Theorem describes an expected distribution shape. Which of these statements is correct?

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 standard deviation of the sample means is the same as that of the population. Reason: The sample means have smaller variation than the population means because the sample means are found by averaging n observations from the population.

Pick the statement that describes the formula for the standard error of the mean in ordinary language.

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

Which of the populations listed below is a natural candidate for cluster sampling?

The voters in a state, who are grouped into political districts.

Which of the following is a systematic random sample random sample? Choose one.

To verify the accuracy of a automated beverage filling line, every 30th can is selected and weighed.

There are two conditions under which we can assume that the sample means follow a normal distribution. What are they?

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

When is it inappropriate to use systematic random sampling?

When the order of items in the population is related to some particular characteristic.

How is a table of random numbers used to select a random sample? Choose the steps that make up the process.

numbers are chosen systematically from the random number table items whose numbers correspond to random numbers become the sample Items from the population are assigned sequential numbers.

Which of the following are true regarding parameters and statistics?

μ is a parameter and s^2 is a statistic.