Hypothesis Tests: Classical and pValue Approaches March 22, 2017 9.2 & 9.3 Critical Value vs Pvalue Approach GOALS: 1. Understand the 2 approaches of 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) Class Notes: Prof. G. Battaly, Westchester Community College, NY Class Notes Statistics Home Page 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 2017 © Gertrude Battaly 2014 Class Notes Homework 1 Hypothesis Tests: Classical and pValue Approaches March 22, 2017 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 compares test statistic to critical value compares area beyond test statistic to α 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 2017 © Gertrude Battaly 2014 Class Notes Homework 2 Hypothesis Tests: Classical and pValue Approaches March 22, 2017 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 Further into the tail than is required by α, so we have better data than is required to reject! α z = 1.84 P = normalcdf (9,1.84,0,1) = 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 2017 ©Gertrude Battaly, 2012 Class Notes 3 Hypothesis Tests: Classical and pValue Approaches March 22, 2017 9.2 & 9.3 Critical Value vs Pvalue Approach G: 2tailed test, z = 3.08 F: P; at 5% signif level, can reject H0? Note that have multiplied by 2, because it is a 2tailed test. > If you find p using normalcdf, you need to multiply by 2 for every 2tailed test. > If you use STATS/TEST, the calculator does the multiplication. Class Notes: Prof. G. Battaly, Westchester Community College, NY Class Notes © Gertrude Battaly 2014 Statistics Home Page 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 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 . G: P Values below F: the strength of the evidence against the null hypothesis, H 0? 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 2017 © Gertrude Battaly 2014 Class Notes Homework 4 Hypothesis Tests: Classical and pValue Approaches March 22, 2017 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 . G: P Values below F: the strength of the evidence against the null hypothesis, H 0? a) P = 0.184 ____none_____ b) P = 0.086 ___moderate_____ c) P = 0.001 __ very strong __ d) P = 0.012 ___strong______ Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page ©G. Battaly 2017 © Gertrude Battaly 2014 Class Notes Homework 5
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