Examples of sample in the following topics:

 Recognize the characteristics of a sampling distribution
The sampling distribution of a statistic is the distribution of the statistic for all possible samples from the same population of a given size.
 The sampling distribution depends on: the underlying distribution of the population, the statistic being considered, the sampling procedure employed, and the sample size used.
 Similarly, if you took a second sample of 10 women from the same population, you would not expect the mean of this second sample to equal the mean of the first sample.
 Each sample has its own average value, and the distribution of these averages is called the "sampling distribution of the sample mean
 An alternative to the sample mean is the sample median.
 inferential statistics (noun) A branch of mathematics that involves drawing conclusions about a population based on sample data drawn from it.
 sampling distribution (noun) The probability distribution of a given statistic based on a random sample.

 This process of collecting information from a sample is referred to as sampling.
 The best way to avoid a biased or unrepresentative sample is to select a random sample, also known as a probability sample.
 Several types of random samples are simple random samples, systematic samples, stratified random samples, and cluster random samples.
 A sample that is not random is called a nonrandom sample, or a nonprobability sampling.
 Some examples of nonrandom samples are convenience samples, judgment samples, and quota samples.
 population (noun) a group of units (persons, objects, or other items) enumerated in a census or from which a sample is drawn

 Differentiate between a frequency distribution and a sampling distribution
Learn to create a sampling distribution from a discrete set of data.
 As the number of samples approaches infinity, the frequency distribution will approach the sampling distribution.
 Specifically, it is the sampling distribution of the mean for a sample size of 2 (N=2).
 This process is repeated for a second sample, a third sample, and eventually thousands of samples.
 As the number of samples approaches infinity , the frequency distribution will approach the sampling distribution.
 sampling distribution (noun) The probability distribution of a given statistic based on a random sample.

 Categorize a random sample as a simple random sample, a stratified random sample, a cluster sample, or a systematic sample
A random sample, also called a probability sample, is taken when each individual has an equal probability of being chosen for the sample.
 Also commonly referred to as a probability sample, a simple random sample of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance of being in the selected sample.
 At this stage, a simple random sample would be chosen from each stratum and combined to form the full sample.
 Each sample would be combined to form the full sample.
 In this case, k=population size/sample size.
 population (noun) a group of units (persons, objects, or other items) enumerated in a census or from which a sample is drawn

 The student will demonstrate the simple random, systematic, stratified, and cluster sampling techniques.
 In this lab, you will be asked to pick several random samples.
 Pick a simple random sample of 15 restaurants.
 Fill in the table above
Pick a systematic sample of 15 restaurants.
 Fill in the table above
Pick a stratified sample, by city, of 20 restaurants.

 The motivation in Chapter 4 for requiring a large sample was twofold.
 First, a large sample ensures that the sampling distribution of $\bar{x}$ is nearly normal.
 The second motivation for a large sample was that we get a better estimate of the standard error when using a large sample.
 We will see that the t distribution is a helpful substitute for the normal distribution when we model a sample mean $\bar{x}$ that comes from a small sample.
 While we emphasize the use of the t distribution for small samples, this distribution may also be used for means from large samples.

 Distinguish between probability samples and nonprobability samples for surveys
When conducting a survey, a sample can be chosen by chance or by more methodical methods.
 Probability sampling includes simple random sampling, systematic sampling, stratified sampling, and cluster sampling.
 Probability sampling includes: Simple Random Sampling, Systematic Sampling, Stratified Sampling, Probability Proportional to Size Sampling, and Cluster or Multistage Sampling.
 Hence, because the selection of elements is nonrandom, nonprobability sampling does not allow the estimation of sampling errors.
 Nonprobability sampling methods include accidental sampling, quota sampling, and purposive sampling.
 purposive sampling (noun) occurs when the researchers choose the sample based on who they think would be appropriate for the study; used primarily when there is a limited number of people that have expertise in the area being researched

 In survey sampling, weights can be applied to the data to adjust for the sample design, particularly stratified sampling (blocking).
 Simple random sampling is a basic type of sampling, since it can be a component of other more complex sampling methods.
 Further, for a small sample from a large population, sampling without replacement is approximately the same as sampling with replacement, since the odds of choosing the same individual twice is low.
 Conceptually, simple random sampling is the simplest of the probability sampling techniques.
 If these conditions are not true, stratified sampling or cluster sampling may be a better choice.
 population (noun) a group of units (persons, objects, or other items) enumerated in a census or from which a sample is drawn
 random sample (noun) a sample randomly taken from an investigated population

 Twosample tests are appropriate for comparing two samples, typically experimental and control samples from a scientifically controlled experiment.
 Onesample tests are appropriate when a sample is being compared to the population from a hypothesis.
 Twosample tests are appropriate for comparing two samples, typically experimental and control samples from a scientifically controlled experiment.
 Rather than comparing two sets, members are paired between samples so the difference between the members becomes the sample.
 This formula will calculate a tstatistic for a onesample ttest, where x(bar) = sample mean, mu = population mean, s = sample standard deviation and n = sample size.

 Describe the general properties of sampling distributions
Analyze how close your sample mean is to the population mean by using the standard error
Knowledge of the sampling distribution can be very useful in making inferences about the overall population.
 The most common measure of how much sample means differ from each other is the standard deviation of the sampling distribution of the mean.
 For the case where the statistic is the sample mean, and samples are uncorrelated, the standard error is:
This image shows the formula use to calculate the standard error of the mean,wheresis the sample standard deviation andnis the size (number of items) in the sample.
where s is the sample standard deviation and n is the size (number of items) in the sample.
 This spread is determined by the sampling design and the size of the sample.
 Larger samples give smaller spread.
 sampling distribution (noun) The probability distribution of a given statistic based on a random sample.
 inferential statistics (noun) A branch of mathematics that involves drawing conclusions about a population based on sample data drawn from it.