9.2 & 9.3 Critical Value vs P
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Hypothesis Testing: Critical Value vs. P­Value Approach November 04, 2015 9.2 & 9.3 Critical Value vs P­value Approach GOALS: 1. Learn the 2 approaches used for hypothesis testing: classical or critical value, and p­value. 2. Understand the critical value for hypothesis testing is the same zα/2 or tα/2 used in finding Confidence Intervals. 3. Learn the p­value as the observed significance. 4. Find the p­value for 1­tailed and 2­tailed tests. Study Ch. 9.3, #47­53 (45­51), 55­61, 63­67 (55­59)­59 Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © Gertrude Battaly 2014 Class Notes Homework 9.2 & 9.3 Critical Value vs P­value Approach Hypothesis Testing: attempt to determine if sample data is different from a previously known or expected value. H0: μ = μ0 Start with an assumption that sample data equals the known or expected values. What do we use to decide? distribution of x μ x σx How do we decide? 2 different approaches Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © G. Battaly 2015 © Gertrude Battaly 2014 Class Notes Homework 1 Hypothesis Testing: Critical Value vs. P­Value Approach November 04, 2015 9.2 & 9.3 Critical Value vs P­value Approach Approach Critical Value P­Value (table based, can use calculator) (calculator based, can use table) 1. State the Null and Alternative Hypotheses: H0,Ha 2. Decide the significance level, α, and sketch Ha: μ < μ0 α Ha: μ ≠ μ0 α/2 Ha: μ > μ0 α/2 α 3. Compute the test statistic: z, t, etc. 4. Find the critical values Find the P­value zα, zα/2, tα , tα/2 5. Decision: Rej. H0 if test Decision: Rej. H0 if statistic lies beyond critical P ≤ α value in rejection region 6. Interpret results Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © Gertrude Battaly 2014 Class Notes Homework 9.2 & 9.3 Critical Value vs P­value Approach Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © G. Battaly 2015 © Gertrude Battaly 2014 Class Notes Homework 2 Hypothesis Testing: Critical Value vs. P­Value Approach November 04, 2015 9.2 & 9.3 Critical Value vs P­value Approach P­Value: observed significance 1. area in the tail beyond the test statistic 2. smallest significance level for rejecting H0 G: left­tailed test, z = ­1.84 F: P; at 5% signif level, can reject H0? P α z = ­1.84 P = normalcdf (­5,­1.84,0,1) = 0.0329 P = 0.0329 < 0.05 Therefore, reject H0. Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © Gertrude Battaly 2014 Class Notes Homework Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page Class Notes ©Gertrude Battaly, 2012 9.2 & 9.3 Critical Value vs P­value Approach G: 2­tailed test, z = 3.08 F: P; at 5% signif level, can reject H0? normalcdf (______,_____,0,1) = ______ P = 2 (________) = ______ P = _____ __ 0.05 Therefore, ___________ H0. < > Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © Gertrude Battaly 2014 Class Notes Homework Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © G. Battaly 2015 ©Gertrude Battaly, 2012 Class Notes 3 Hypothesis Testing: Critical Value vs. P­Value Approach November 04, 2015 9.2 & 9.3 Critical Value vs P­value Approach p. 378 #58a. G: 2­tailed test, z = 3.08 F: P; at 5% signif level, can reject H0? Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page Class Notes © Gertrude Battaly 2014 Homework Class Notes: Prof. G. Battaly, Westchester Community College, NY Class Notes ©Gertrude Battaly, 2012 Statistics Home Page 9.2 & 9.3 Critical Value vs P­value Approach P­Value and Strength of Evidence P­Value Evidence against H0 p > 0.10 None or Weak 0.05 < p ≤ 0.10 Moderate 0.01 < p ≤ 0.05 Strong p ≤ 0.01 Very Strong p. 378 #54. G: P ­ Values below F: the strength of the evidence against the null hypothesis, H0? a) P = 0.184 _________________ b) P = 0.086 _________________ c) P = 0.001 _________________ d) P = 0.012 _________________ Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © G. Battaly 2015 © Gertrude Battaly 2014 Class Notes Homework 4
