It is commonly
believed that anyone who tabulates numbers is a statistician.
This is like believing that anyone who owns a scalpel is a surgeon.
TWO METHODS FOR INFERENCE:
CONFIDENCE INTERVALS are used to estimate the "value" of a population parameter.
The interval establishes boundaries between which we can have a specified level of confidence about our parameter of interest. There are different levels of confidence and we will use the most common ones and also learn to calculate any desired level.
TESTS of SIGNIFICANCE assess the evidence for a "claim" about the population as a result of gathered data. These tests determine whether the results can be explained by chance occurrence or not and whether the results differ enough from chance to be statistically significant.
procedures are based on sampling distributions, from sample proportions or
sample means, and report the probabilities that state what would happen if we
used inference methods many times. Long run regular behavior is required.
Inference is most reliable when data comes from RANDOMIZED samples.
We must rely on previously learned concepts especially normal distributions and the Central Limit Theorem as we move forward with our logic. We also will rely on standard deviation of the sample = standard deviation of the population divided by the square root of N (number of trials in the sample).
When we make a claim about a population parameter we can say that the parameter is "somewhere around" our sample statistic. SOMEWHERE AROUND is not precise enough. A better question would be "How would the sampling statistic vary if we took many samples of equal size from the same population."
We will be developing many mathematical formulas and using reasoning skills throughout our study of inference.