Chapter 7 - Samples and the Sampling Distribution of the Means Flashcards
What are arguably the most important concepts in statistics?
The sampling distribution of the means and the central limit therorem that describes it.
What are the three major concepts in statistics?
- Distribution of a variable.
- The sampling distribution of the means (and how it is related to the distribution of the variable).
- The test statistic (and how it is related to the distribution of the means).
What three important important characteristics of the sampling distribution does the central limit theorem specify?
Distribution of sample means is:
- normally distributed (if n is sufficiently large) regardless of the shape of the distribution of the original variable.
- has a mean equal to the mean of the variable.
- has a standard deviation (called “the standard error of the mean”) equal to the standard deviation of the variable divided by the square root of the sample size.
What are representative samples?
A sample of a population that reflects the characteristics of the parent population.
What is the central limit theorem?
The theorem that describes the shape, mean, and variation of the sampling distribution of the means.
What is a random sample?
A subset of a population chosen so that each member of a population has an equal chance of being included in the sample, and the selection of each member is independent of whether or not any other particular member is selected. This means that investigators must set aside their own preferences or conveniences and use some purely chance method to select the sample from the target population.
What are the dangers of choosing a sample that does not represent the population?
-Unforeseen bias can creep into selection procedure which can cause your results to be inaccurate. E.g. The Literary Digest 1936 and US government 1960s.
State two ways representative samples can be chosen.
- Simple random sampling
- Stratified random sampling
What is simple random sampling?
A random sampling technique whereby all members of the population are treated equally regardless of their characteristics. It is the most straightforward and frequently used method of obtaining a representative sample.
What is the sampling distribution of the means?
The distribution formed by taking repeated samples from the same population, computing the mean of each sample, and forming the distribution of those sample means.
What two factors affect the magnitude of the standard error or the mean?
The standard deviation and the sample size.
What is a frequent mistake when using the table of random digits (for simple random sampling)?
Forgetting to discard a number that was already used.
What is stratified random sampling?
A sampling procedure whereby the population is divided into subgroups (strata) whose members have the same or similar characteristics, and then simple random samples are taken from each stratum. Sample sizes are proportional to population strata sizes.
What is the standard error of the mean?
The standard deviation of the sampling distribution of the means.
What does the central limit theorem state about shape?
- As the sample size n increases, the sampling distribution of the means of samples of size n approaches a normal distribution.
- The distribution of means of even bimodal, nonasymptotic distribution becomes normal as the sample size increases. Even if the parent population is utterly nonnormal, the distribution of means of samples drawn from that population will be normal if the sample size is large.
