Reading 8: Hypothesis Testing

Book 1: Quantitative Methods

Hypothesis Testing Procedure

1.) State the hypothesis

2.) Select appropriate test statistic

3.) Specify the level of significance

4.) State the decision rule regarding the hypothesis

5.) Collect the sample and calculate the sample statistics

6.) Make a decision regarding the hypothesis

7.) Make a decision based on the results of the test

Which hypothesis is tested—null or alternative?

Null

True or False: “=” is always included in the null.

TRUE

The null and alternative are ________________ and ___________.

mutually exclusive, exhaustive

Mutually exclusive

no possible outcome of the test satisfies both hypotheses

Exhaustive

includes all possible outcomes of the test

Critical value for a 2-tailed 10% sig, 1-tailed 5% sig

1.65

Critical value for a 2-tailed 5% sig, 1-tailed 2.5% sig

1.96Critical value for a 2-tailed 10% sig, 1-tailed 5% sig

Critical value for a 1-tailed 1% sig

2.33

Critical value for a 2-tailed 1% sig

2.58

Type I Error

rejection of the null when it is true

Type II Error

failure to reject the null when it is false

Significance Level (alpha)

the probability of making a Type I error

Power

the probability of correctly rejecting the null when it is false

Tradeoffs (3) for decreasing Type I and Type II error probabilities

1.) Decreasing Type I error increases Type II error

• Vice Versa applies

2.) To increase power, have to increase Type I error probability

3.) You can decrease both Type I and Type II by increasing sample size

What determines the probability of a Type II error?

sample size and significance level

P-Value

the probability of obtaining a test statistic that would lead to a rejection of the null assuming the null is true

• Not the same as Type I errorParam

Parametric Test

tests that rely on assumptions of the dsitribution of the population and are specific to population parameters

Example of parametric test

Z-Test

Nonparametric Test

tests that do not consider a population parameter or have few assumptions about the population being sampled

Runs Test

an estimate of the probability that a series of changes are random