Sampling Distributions

There are two basic questions asked by inferential statistics:

1. How close is the value of a statistic to the corresponding parameter of the entire population. For example, if we have a sample of 30 elements from a population and we find that , we would like to know how far this might be from the mean of the entire population.
2. In many cases, someone has hypothesized a particular value for the parameter of a population or some relationship between the parameters of two or more populations. For example, experience may show that the mean IQ of all people is 100 and someone may want to test whether a particular teaching method leads to higher mean IQ. Similarly, someone may wonder if mean IQ of men (call it ) is the same as that for women (call it ).

Both of these inferential questions are answered using an idea called the sampling distribution of a transformed statistic which we study in this section.

• Statistics and Random Samples
• Sampling Schemes and Inferences from Samples
• The Central Limit Theorem
• Normal Approximation to Binomial
• The Transformed Statistics: Z, t, , F
• Sampling Distributions of the Transformed Statistics