8.1-8.2 - Section 8.1, 8.2, and 8.4 Testing Statistical...

This preview shows pages 1–4. Sign up to view the full content.

Section 8.1, 8.2, and 8.4 Testing Statistical Hypotheses (TSH) 1. Basic Concepts of TSH Estimation deals with obtaining a plausible estimate of θ or obtaining a plausible interval (random) which contains . TSH deals with how to make a decision between two competing claims (hypotheses). Definition : Statistical hypothesis or simply a hypothesis is an assertion about one or more population characteristics or about the form of population distribution. Examples: (i) Let p = proportion of students having cases Hypothesis: .6 p . (ii) Let X = height of the students Hypothesis: 5) (170, ~ N X Kinds of hypotheses: Null hypothesis 0 H is a hypothesis which is initially assumed to be true. Alternative hypothesis a H is the hypothesis compared against 0 H . 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
A test of hypothesis is a method or procedure of deciding between 0 H and a H , based on the sample information. If sample contains strong evidence against 0 H , then it will be rejected in favor of a H . Otherwise, we will continue to believe in 0 H . Hypothesis always refer to some population or model, not to a particular outcome. For this reason, we must state H 0 and H a in terms of population parameters. Example : Suppose 10) , ( ~ μ N X , consider testing (i) 50 : 0 = H against 50 : 1 < H (lower-tailed) or 50 : a H (upper-tailed) (ii) 50 : 0 = H against 50 : a H (two-tailed). A test leads to one of the following decisions (i) Fail to reject 0 H (ii) Reject 0 H (Accept a H ) Obviously, we have two-kinds of errors inherent in any test. 2
Definition: Type I error Reject 0 H when 0 H is true. Type II error Fail to reject 0 H when a H is true. Definition: P(Type I error) = α = P (Reject 0 H when 0 H is true). P(Type II error) = β = P(Fail to reject 0 H when a H is true). It can be shown that both errors and can not be minimized. Usually, we fix one of the errors, say , and choose a test that minimizes . In practice, = .05 or = 0.01, is chosen. Definition: The specified value of is also called “level of significance” or “significance level of the test”. Remarks : (i) A test with significance level = .05 means that when the test repeated several times, only 5% of times it may commit the type I error. (ii) The quantity (1- ) = P (Reject 0 H when a H is true) is called the power of the test .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

8.1-8.2 - Section 8.1, 8.2, and 8.4 Testing Statistical...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online