Week 14 Mon Nov 29a - Posted after class WEEK 14 Mon Nov 29...

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1 Posted after class. WEEK 14 – Mon, Nov 29 HYPOTHESIS TESTING – Critical Value Approach (Background material is in Chapter 7) Tests for Mean μ Population Standard Deviation σ Known - a z-test. The test statistic is where or The textbook ignores the size of the population and on p. 272 shows the test statistic as without displaying the subscript on μ. Steps for an α-level, right-tailed z-test of H 0 : μ ≤ μ 0 v. H 1 : μ > μ 0 . a. Determine the critical value for z, namely, c = z α . b. Gather the data, determine . Calculate z. c. Compare the observed z to the critical value. If z > z α , Reject H 0 in favor of H 1 . If z ≤ z α , Retain H 0 . Steps for an α-level, left-tailed z-test of H 0 : μ ≥ μ 0 v. H 1 : μ < μ 0 . a. Determine the critical value for z, namely, c = -z α . b. Gather the data, determine . Calculate z. c. Compare the observed z to the critical value. If z < -z α , Reject H 0 in favor of H 1 . If z ≥ -z α , Retain H 0 . Steps for an α-level, two-tailed z-test of H 0 : μ = μ 0 v. H 1 : μ ≠ μ 0 . a. Determine the critical values for z, namely, c 1 = -z α/2 and c 2 = z α/2 . b. Gather the data, determine . Calculate z. c. Compare the observed z to the critical values. If either z < -z α/2 or z > z α/2 , Reject H 0 in favor of H 1 . If -z α/2 ≤ z ≤ z α/2 , Retain H 0 .
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2 Population Standard Deviation σ Unknown - a t-test. The test statistic is where or The textbook ignores the size of the population and on p. 272 shows the test statistic as without displaying the subscript on μ. Steps for an α-level, right-tailed t-test of H 0 : μ ≤ μ 0 v. H 1 : μ > μ 0 . a. Determine the critical value for t, namely, c = t α based on n – 1 df . b. Gather the data, determine and s. Calculate t. c. Compare the observed t to the critical value. If t > t α , Reject H 0 in favor of H 1 . If t ≤ t α , Retain H 0 . Steps for an α-level, left-tailed t-test of H 0 : μ ≥ μ 0 v. H 1 : μ < μ 0 . a. Determine the critical value for t, namely, c = -t α based on n – 1 df . b. Gather the data, determine and s. Calculate t. c. Compare the observed t to the critical value. If t < -t α , Reject H 0 in favor of H 1 . If t ≥ -t α , Retain H 0 . Steps for an α-level, two-tailed t-test of H 0 : μ = μ 0 v. H 1 : μ ≠ μ 0 . a. Determine the critical values for t, namely, c 1 = -t α/2 and c 2 = t α/2 , based on n – 1 df . b. Gather the data, determine and s. Calculate t. c. Compare the observed t to the critical values. If either t < -t α/2 or t > t α/2 , Reject H 0 in favor of H 1 . If -t α/2 ≤ t ≤ t α/2 , Retain H 0 . Note
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This note was uploaded on 02/01/2011 for the course STAT 315 taught by Professor Dennisgilliland during the Summer '10 term at Michigan State University.

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Week 14 Mon Nov 29a - Posted after class WEEK 14 Mon Nov 29...

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