Module 10.1: Central Limit Theorem and Standard Error Flashcards
What is simple random sampling?
What is systemic sampling?
A method of selecting a sample in such a way that each item or person in the population being studied has the same likelihood of being included in the sample.
Systemic sampling is picking every nth number from a population.
What is sampling error? What is the formula?
The difference between a sample statistic and its corresponding population parameter. For example, the sampling error for the mean is as follows:
Sampling error of the mean = sample mean - population mean
What is the sampling distribution?
Is the probability of all possible sample statistics computed from a set of equal size samples that were randomly drawn from the same population.
What is stratified random sampling?
Uses a classification to separate the population into smaller groups based on one or more distinguishing characteristic. For example, the bond market is typically stratified by yield, duration, maturity etc and then a sample is taken.
What is time series data?
Consist of observations taken over a period of time at specific and equally spaced time intervals.
What is cross-sectional data?
sample of observations taken at a single point in time.
What is longitudinal data?
What is Panel Data?
Time-series data and cross-sectional data combined such as unemployment, inflation, GDP.
Panel data contain observation over time of the same characteristic for multiple entities such as debt/ equity ratios for 20 companies.
What is the central limit theorem?
States that for a simple random sample of size n from a population with a mean x and a finite variance o2, the sampling distribution of the sample mean y approaches a normal probability distribution with a mean u and a variance equal to o2 / n.
Specific inferences about the population mean can be made from the sample mean, regardless of the population’s distribution, as long as the sample size is “sufficiently large” n>30.
What are the three important properties of the central limit theorem?
1) If sample size is large, sampling distribution will be approx normal.
2) The mean of the population and the mean of the distribution of all possible sample means are equal.
3) the variance of the distribution of sample means is o2/n, the population variance divided by the sample size.
What is standard error of the sample mean? How is it calculated when the population standard deviation is known? How is it calculated when it is unkown?
Standard error of the sample mean is the standard deviation of the sample means.
When the standard deviation of the population is known, the standard error of the sample mean is calcuated as: standard deviation of pop / square root of n.
If pop standard deviation is unkown, it is standard deviation of the sample / square root of n.
What are the desitable properties of an estiamtor?
1) Unbiased estimator - sample mean is equal to the population mean
2) Efficient - variance of its sampling distribution is smaller than all the other unbiased estiamtors of the parameter you are trying to create.
3) Consistent - the accuracy of the parameter estimate increases as the sample size increases.
