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M 562 Section-10-5

# M 562 Section-10-5 - b&& z ± ± b& ±& Hence...

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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,

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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 & & & ² b & < & z ± Thus, the acceptance region is given by b & & & ² b & ± & z ± or & ² b & + z ± ² b & which is equivalent to an upper-tail con&dence interval for & with con&dence co-e±cient 1 & ± , & ² b & + z ± ² 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...
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M 562 Section-10-5 - b&& z ± ± b& ±& Hence...

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