Hypothesis Testing and Confidence Interval

A population is characterized by numerical descriptive measures called parameters. Most inferential problems can be formulated as an inference about one or more parameters of a population. Generally, there are two types of statistical inferencing – estimation and hypothesis test.

Hypothesis Testing relates to a single conclusion of statistical significance versus no statistical significance. Use hypothesis testing when you are doing a strict comparison with a specified hypothesis and significance.

All hypothesis test problems have the following steps:

-       Write your null (Ho) and alternate hypothesis (Ha).

-       Compute test statistics based on a random sample.

-       Compute p-value.

-       Conclusion.

Confidence Interval falls under statistical inferencing called estimation. It provides a range of plausible values of your population. Use confidence interval when you want to describe a single sample or magnitude of effect. E.g., mean difference.

Scenario: If we collected all possible samples from a given population, and computed confidence intervals for each sample. Some confidence intervals would include the true population parameter and others would not. A 90% confidence level means that 90% of the intervals contain the true population parameter.

Often, the confidence level is denoted by 1 - alpha, where   is the chance that it does not cover the true parameter. For example, if alpha = 0:05, then the confidence level is 0.95, or 95%. We then say that we are 95% confidence that the 95% of all intervals contain true population parameter.

Any confidence interval is of the form:

Confidence Interval = Point Estimate ± Margin of Error (E)

We do not try to have 100% confidence intervals.