stat 250 chapter 8

significance level

- The significance level is the probability of making the mistake of rejecting the null hypothesis when, in fact, the null hypothesis is true. - The symbol for the significance level is α. - For most applications a significance level of 0.05 is used, but 0.01 and 0.10 are also sometimes used.

When conducting a left-tailed hypothesis test, which of the following test statistics would provide the strongest evidence against the null hypothesis? -2.78 -1.64 .001 2.95

-2.78

hypothesis testing

A procedure that enables us to choose between two claims when we have variability in our measurements. Purpose - to aid investigators in reaching a decision concerning a population by examining the data obtained from a sample Goal - to assess the evidence provided by the data in favor of some claim about the population

Interpreting p-values

A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

In hypothesis testing there is strong evidence against the null hypothesis if the p-value is

Close to 0.

In hypothesis testing, if the null hypothesis is true, the test statistic will be Close to 0. Close to 1. Close to the sample statistic. Close to the significance level.

Close to 0.

Hypotheses are always statements about Sample statistics. Population parameters. Either sample statistics or population. Parameters, depending on the context of the problem.

Population parameters.

p-value

The P value, or calculated probability, is the probability of finding the observed, or more extreme, results when the null hypothesis (H 0) of a study question is true

H0 The Null Hypothesis

The neutral, status quo, skeptical statement about a population parameter Always contains =

Ha The Alternative Hypothesis

The research hypothesis; the statement about a population parameter we intend to demonstrate is true Always contains <, >, or ≠ Hypotheses are always about population PARAMETERS; they are never about sample statistics.