Learning Objectives Describe the hypothesis testing process Distinguish the types of hypotheses Explain hypothesis testing errors Solve hypothesis testing problems – One population mean – One population proportion – One & two-tailed tests

Statistical Methods

What’s a Hypothesis? A belief about a population parameter – Parameter is population mean, proportion, variance – Must be stated before analysis I believe the mean GPA of this class is 3.5! © T/Maker Co.

Null Hypothesis What is tested Has serious outcome if incorrect decision made Always has equality sign: ,  or  Designated H 0 – Pronounced ‘H sub-zero’ or ‘H oh’ Example – H 0 :   3

Alternative Hypothesis Opposite of null hypothesis Always has inequality sign: , , or  Designated H 1 Example – H 1 :  < 3

Basic Idea Sampling Distribution It is unlikely that we would get a sample mean of this value if in fact this were the population mean... therefore, we reject the hypothesis that  = H0H0H0H0 H0H0H0H0

Level of Significance Defines unlikely values of sample statistic if null hypothesis is true – Called rejection region of sampling distribution Designated  (alpha) – Typical values are.01,.05,.10 Selected by researcher at start

Rejection Region (One-Tail Test) Sampling Distribution 1 -  Level of Confidence

Rejection Regions (Two-Tailed Test) Sampling Distribution 1 -  Level of Confidence

Errors in Making Decision Type I error – Reject true null hypothesis – Has serious consequences – Probability of Type I error is  Called level of significance Type II error – Do not reject false null hypothesis – Probability of Type II error is  (Beta)

Decision Ho: Ha: Truth

Decision Results H 0 : Innocent

 &  Have an Inverse Relationship   You can’t reduce both errors simultaneously!

H 0 Testing Steps Set up critical values Collect data Compute test statistic Make statistical decision Express decision n State H 0 n State H 1 Choose  Choose  n Choose n n Choose test

p-Value Probability of obtaining a test statistic more extreme (  or  than actual sample value given H 0 is true Called observed level of significance – Smallest value of  H 0 can be rejected Used to make rejection decision – If p-value  , do not reject H 0 – If p-value < , reject H 0