Examples of sample in the following topics:

 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.

 The sampling distribution of a statistic is the distribution of the statistic for all possible samples from the same population of a given size.
 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.
 Sampling distributions allow analytical considerations to be based on the sampling distribution of a statistic rather than on the joint probability distribution of all the individual sample values.
 The sampling distribution depends on: the underlying distribution of the population, the statistic being considered, the sampling procedure employed, and the sample size used.
 Each sample has its own average value, and the distribution of these averages is called the "sampling distribution of the sample mean.

 Twosample ttests for a difference in mean involve independent samples, paired samples, and overlapping samples.
 The two sample ttest is used to compare the means of two independent samples.
 For the null hypothesis, the observed tstatistic is equal to the difference between the two sample means divided by the standard error of the difference between the sample means.
 Twosample ttests for a difference in mean involve independent samples, paired samples and overlapping samples.
 An overlapping samples ttest is used when there are paired samples with data missing in one or the other samples (e.g., due to selection of "I don't know" options in questionnaires, or because respondents are randomly assigned to a subset question).

 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:
 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.
 This image shows the formula use to calculate the standard error of the mean, where s is the sample standard deviation and n is the size (number of items) in the sample.

 The two samples are independent of oneanother, so the data are not paired.
 Because we are examining two simple random samples from less than 10% of the population, each sample contains at least 30 observations, and neither distribution is strongly skewed, we can safely conclude the sampling distribution of each sample mean is nearly normal.
 Finally, because each sample is independent of the other (e.g. the data are not paired), we can conclude that the diﬀerence in sample means can be modeled using a normal distribution.
 If the sample means, $\bar{x}_1$ and $\bar{x}_2$, each meet the criteria for having nearly normal sampling distributions and the observations in the two samples are independent, then the diﬀerence in sample means, $\bar{x}_1\bar{x}_2$, will have a sampling distribution that is nearly normal.
 Because each sample has at least 30 observations (nw = 55 and nm = 45), this substitution using the sample standard deviation tends to be very good.

 In this lab, you will be asked to pick several random samples.
 In each case, describe your procedure briefly, including how you might have used the random number generator, and then list the restaurants in the sample you obtained

 Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample.
 The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample.
 For example, in a survey sampling involving stratified sampling there would be different sample sizes for each population.
 Sample sizes are judged based on the quality of the resulting estimates.
 Solving for n gives you an equation for the sample size, as shown in .

 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.

 Here we consider three random sampling techniques: simple, strati ed, and cluster sampling.
 Simple random sampling is probably the most intuitive form of random sampling.
 Then we sample a fixed number of clusters and collect a simple random sample within each cluster.
 This technique is similar to strati ed sampling in its process, except that there is no requirement in cluster sampling to sample from every cluster.
 Sometimes cluster sampling can be a more economical random sampling technique than the alternatives.

 In this sense, we can say that simple random sampling chooses a sample by pure chance.
 Just this defect alone means the sample was not formed through simple random sampling.
 Sometimes it is not feasible to build a sample using simple random sampling.
 Since simple random sampling often does not ensure a representative sample, a sampling method called stratified random sampling is sometimes used to make the sample more representative of the population.
 In stratified sampling, you first identify members of your sample who belong to each group.