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.



 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 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.



 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.