Sampling Distributions

Question 1

What is the difference between a parameter and a statistic?

Answer 1

A parameter is a mean estimate for a population, and a statistic is a mean estimate for a sample

Question 2

What is a sampling distribution?

Answer 2

The hypothetical mean of a population based on a sample, where the statistic is the variable of interest

Question 3

What are the three properties of the sampling distribution?How does this chance when we look at bivariate analysis and t-tests?

Answer 3

1. The mean of the sampling distribution (the mean of means) is the mean of the population.
2. The standard deviation of the sampling distribution is called the standard error of the mean
3. When the sample size (n) is large, the sampling distribution appears normal.
   For bivariate analysis, we are concerned with the EFFECT that the independent variable has on the dependent variable
   For T-tests (comparison of two means) we are concerned with the difference between the two means

Question 4

What are confidence intervals?

Answer 4

When we make a statistic, we can choose to do a point estimate or an interval estimate. A point estimate is where we claim that the statistic is the parameter of the population. An interval estimate is where we create a range, and claim that the parameter is somewhere within that range. This is a confidence interval. The interval size depends on:

1. Level of confidence: This is based off of our standard deviation from the mean (standard error). We typically go by 2 standard errors, so we have a 95% chance of getting the parameter within our interval. If we did it between 1 standard error, we would only have a 68% chance.
2. Standard error size: The bigger your standard error, the larger your interval! Your z-score is the size of your standard error