UASTAT151Ch9 - 9.1 Hypotheses and Test Procedures Defn A...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
9.1 Hypotheses and Test Procedures Def’n: A null hypothesis is a claim about a population parameter that is assumed to be true until it is declared false. An alternative hypothesis is a claim about a population parameter that will be true if the null hypothesis is false. In carrying out a test of H 0 vs. H A , the hypothesis H 0 is “rejected” in favour of H A only if sample evidence strongly suggests that H 0 is false. If the sample does not contain such evidence, H 0 is “not rejected” or you “fail to reject” it. NEVER “accept” H 0 or H A …for different reasons. Ex9.1) H 0 : μ = 2.8 H A : μ 2.8 pop’n characteristic hypothesized value or “claim” Def’n: A two-tailed test has “rejection regions” in both tails. A one-tailed test has a “rejection region” in one tail. A lower-tailed test has the “rejection region” in the left tail. An upper-tailed test has the “rejection region” in the right tail. Ex9.2) a) H 0 : μ = 15 H A : μ = 15 Æ INCORRECT b) H 0 : μ = 123 H A : μ = 125 Æ INCORRECT c) H 0 : μ = 123 H A : μ < 123 Æ CORRECT d) H 0 : p = 0.4 H A : p > 0.6 Æ INCORRECT e) H 0 : p = 1.5 H A : p > 1.5 Æ INCORRECT f) H 0 : p ˆ = 0.1 H A : p ˆ 0.1 Æ INCORRECT Two-Tailed Test Lower-Tailed Test Upper-Tailed Test Sign for H 0 = = or = or Sign for H A < > “Rejection region” In both tails In the left tail In the right tail Ex9.3) Is the mean different than μ 0 ? H 0 : μ = μ 0 H A : μ μ 0 Is the mean lower than μ 0 ? H 0 : μ μ 0 H A : μ < μ 0 Is the mean lower or still the same than μ 0 ? H 0 : μ μ 0 H A : μ > μ 0 Is the mean higher than μ 0 ? H 0 : μ μ 0 H A : μ > μ 0 Def’n: A test statistic is the function of the sample data on which a conclusion to reject or fail to reject H 0 is based. For example, Z and t are test statistics. The p -value is a measure of inconsistency between the hypothesized value for a pop’n characteristic and the observed sample. Assuming H 0 is true, the p -value can be defined as the probability of obtaining a test statistic value at least as inconsistent with H
Background image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 4

UASTAT151Ch9 - 9.1 Hypotheses and Test Procedures Defn A...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online