M 562 Section-10-5

M 562 Section-10-5 - b & & z b...

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

View Full Document Right Arrow Icon
MTH/STA 562 RELATIONSHIP BETWEEN HYPOTHESIS TESTING PROCEDURES AND CONFIDENCE INTERVALS As usual, let b denote an unbiased estimator of the unknown parameter with standard error ± b . (1) ( Two-tailed Test ) The rejection region for testing H 0 : = & 0 against H a : 6 = & 0 (where & 0 ) at level ² is given by b & 0 ± b > z ±= 2 Thus, the acceptance region is given by b & 0 ± b ± z ±= 2 or b z ±= 2 ± b ± & 0 ± b + z ±= 2 ± b with con&dence coef- ² , that is, b z ±= 2 ± b ± ± b + z ±= 2 ± b Hence, we would reject the null hypothesis H 0 : = & 0 in favor of the alternative hypothesis H a : 6 = & 0 if b (2) ( Upper-tail Test ) The rejection region for testing H 0 : = & 0 against H a : & > & 0 (where & 0 ) at level ² is given by b & 0 ± b > z ± Thus, the acceptance region is given by b & 0 ± b ± z ± or b z ± ± b ± & 0 with con&dence coe±- cient 1 ² , that is,
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: b & & z b & & Hence, we would reject the null hypothesis H : & = & in favor of the alternative hypothesis H a : & > & if b & lies outside the lower-tail con&dence interval. . (3) ( Lower-tail Test ) The rejection region for testing H : & = & against H a : & < & (where & is a speci&ed values of & ) at level is given by b & & & b & < & z Thus, the acceptance region is given by b & & & b & & z or & b & + z b & which is equivalent to an upper-tail con&dence interval for & with con&dence co-ecient 1 & , & b & + z b & Hence, we would reject the null hypothesis H : & = & in favor of the alternative hypothesis H a : & 6 = & if b & lies outside the upper-tail con&dence interval. 2...
View Full Document

This note was uploaded on 04/20/2008 for the course MTH 562 taught by Professor Cheng during the Spring '08 term at Creighton.

Page1 / 2

M 562 Section-10-5 - b & & z b...

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