Hypothesis Testing

A Type I Error is rejecting the null hypothesis--H₀--when it is actually true. The significance level is the probability of a Type I Error.

A Type II Error is failing to reject the H₀ when it is actually false. The power of test is 1 - Probabilty of a Type II Error.

There is a tradeoff for trying to minimize the chance of one of these errors. For a given sample size, decreasing the probability of a Type I Error increases the probability of Type II Error and vice versa.

A test statistic is a quantity calculated from a sample whose value is the basis for deciding whether or not to reject the null hypothesis.

Hypothesis testing is the statistical assessment of a statement on a population. Hypothesis testing procedures help determine whether a hypothesis is a reasonable statement that shouldn't be rejected or a stupid idea that should be tossed out ASAP.

The Student's T-distrubution is a symmetrical distribution that is largely used to make inferences regarding the mean of a normal distribution whose variance is unnkown or when working with a small sample size.

The t-distrubtion is less peaked and has fatter tails than a standard normal distrubiton. This makes it a more conservative measure for constructing confidence intervals for the population mean.

Properties

The student's T-distrubtion is