What is a hypothesis?

A claim or statement about a particular characteristic of a population

What is a hypothesis test also called?

A test of significance

What is a hypothesis test?

A procedure for testing a claim about a population.

What is used to perform a hypothesis test?

A sample result

What is the rare event rule?

If, under a given assumption, the probability of a particular observed event is small, we conclude the assumption may not be correct.

What is the Null Hypothesis?

The assumption that the variable has no effect or no difference

What is the shorthand way of representing the Null Hypothesis?

H_{0}

What is the Alternate Hypothesis?

The assumption that the variable has and effect or a difference

What are two shorthand ways to represent the Null Hypothesis?

H_{1}

H_{A}

What is a Type I Error?

You reject H_{0} as being false when it is actually true.

What is a Type II Error?

You fail to reject H_{0} as being true when it is actually false.

Which error is more significant: Type I or Type II?

A Type I error

What is the shorthand way to represent the significance level?

α

What is the significance level?

The probability of making a Type I error

What is the most common significance level?

0.05 (5%)

What does a test statistic (calculated from sample data) measure?

How far the data diverges from the null hypothesis H_{0}

What is a P-Value?

The probability that the test statistic would take a value as extreme or more extreme than that actually observed.

What is a P-Value calculated assuming?

H_{0} is true

How does a P-value relate to the strength of the evidence of data?

The smaller the P‐value, the stronger the evidence against H_{0} provided by the data.

What is the rejection region?

Each tail (of the size ^{α}/_{2}) outside of 1-α

If the Z-Test Statistic lies within the rejection region, is there enough evidence to reject the null hypothesis?

Yes

If the Z-Test Statistic lies within the no-rejection region, is there enough evidence to reject the null hypothesis?

No

What are the four steps for tests of significance?

State

Formulate

Solve

Conclude

What question should you ask yourself for the "state" part of the State/Formulate/Solve/Conclude method of significance testing?

What is the practical question that requires a statistical test?

What two things do you need to do for the "formulate" part of the state/formulate/solve/conclude method?

Identify the parameter and state null and alternative hypotheses.

Decide the significance level.

What 4 things must you do in the "solve" part of the State/Formulate/Solve/Conclude method of significance testing?

Carry out the test in two phases.

Check the conditions.

Calculate the test statistic

Obtain the P‐value.

What does "conclude" encompass in the State/Formulate/Solve/Conclude method of significance testing?

Return to the practical question to describe your results.

What formula is the one-sample z-statistic when σ is known given by?

Z=(x̅-μ_{0})/(^{σ}/_{√n})

What are the 3 requirements for a Z-Test about μ when σ is known?

The sample is a simple random sample.

The value of the population standard deviation is known.

The population is Normally distributed, or the sample size n>30

What is the one-sample z-statistic when σ is not known given by?

Z=(x̅-μ_{0})/(^{s}/_{√n})