Study Ch. 9.3, #47 53 (45 51), 55 61, (55 59)

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GOALS: 1. Understand that 2 approaches of hypothesis testing exist: classical or critical value, and p value. We will use the p value approach. 2. Understand the critical value for the classical approach is the same z /2 or t /2 used in finding Confidence Intervals.

1 GOALS: 1. Understand that 2 approaches of hypothesis testing exist: classical or critical value, and p value. We will use the p value approach. 2. Understand the critical value for the classical approach is the same z /2 or t /2 used in finding Confidence Intervals. 3. Learn the p value as the observed significance obtained from the data. 4. Find the p value for 1 tailed and 2 tailed tests. Study Ch. 9.3, #47 53 (45 51), 55 61, (55 59) : rof., Westchester Community College, NY Hypothesis Testing: attempt to determine if sample data is different from a previously known or expected value. H 0 : μ = μ0 Start with an assumption that sample data equals the known or expected values. What do we use to decide? distribution of μ x σ x x How do we decide? 2 different approaches : rof., Westchester Community College, NY

2 Approach Critical Value Value (table based, can use calculator) (calculator based, can use table) 1. State the Null and Alternative Hypotheses: H 0, H a 2. Decide the significance level,, and sketch H a: μ < μ0 H a: μ μ0 H a: μ > μ0 /2 /2 3. Compute the test statistic: z, t, etc. 4. Find the critical values Find the value compares test statistic to critical value z, z /2, t, t /2 5. Decision: Rej. H 0 if test Decision: Rej. H 0 if statistic lies beyond critical value in rejection region 6. Interpret results compares area beyond test statistic to : rof., Westchester Community College, NY value Approach (digital calculator): Determine the area (p) in the tail beyond the test statistic and compare to, the area in the tail associated with the given significance level. z t reject H 0 z t Do NOT reject H 0 p is found by: 1. calculator function or 2. normalcdf(test statistic, 9,0,1) to get area in right tail. normalcdf( 9,test statistic,0,1) to get area in left tail. If test is 2 tailed, double the result : rof., Westchester Community College, NY

z reject H 0 z z t z t Do NOT reject H 0 : rof., Westchester Community College, NY Value: observed significance 1. area in the tail beyond the test statistic 2.

3 z reject H 0 z z t z t Do NOT reject H 0 : rof., Westchester Community College, NY Value: observed significance 1. area in the tail beyond the test statistic 2. smallest significance level for rejecting H 0 G: left tailed test, z = 1.84 F: ; at 5% signif level, can reject H 0? z = 1.84 = normalcdf (,,0,1) = =? 0.05 Therefore, : rof., Westchester Community College, NY

Value: observed significance 1. area in the tail beyond the test statistic 2. smallest significance level for rejecting H 0 G: left tailed test, z = 1.84 F: ; at 5% signif level, can reject H 0?

4 Value: observed significance 1. area in the tail beyond the test statistic 2. smallest significance level for rejecting H 0 G: left tailed test, z = 1.84 F: ; at 5% signif level, can reject H 0? z = 1.84 = normalcdf ( 9, 1.84,0,1) = = < 0.05 Therefore, reject H 0. Further into the tail than is required by, so we have better data than is required to reject! Our data represents a lower significance and a higher confidence: 96.7% confidence > 95% confidence : rof., Westchester Community College, NY G: 2 tailed test, z = 3.08 F: ; at 5% signif level, can reject H 0? normalcdf (,,0,1) = = 2 ( ) = = 0.05 Therefore, H 0. < > : rof., Westchester Community College, NY

5 G: 2 tailed test, z = 3.08 F: ; at 5% signif level, can reject H 0? Area in right tail Area in both tails Note that have multiplied by 2, because it is a 2 tailed test. > If you find p using normalcdf, you need to multiply by 2 for every 2 tailed test. > If you use STATS/TEST, the calculator does the multiplication. : rof., Westchester Community College, NY Value and Strength of Evidence Value Evidence against H 0 p > 0.10 None or Weak 0.05 < p 0.10 Moderate 0.01 < p 0.05 Strong p 0.01 Very Strong. G: Values below F: the strength of the evidence against the null hypothesis, H 0? a) = b) = c) = d) = : rof., Westchester Community College, NY

6 Value and Strength of Evidence Value p > 0.10 None or Weak 0.05 < p 0.10 Moderate 0.01 < p 0.05 Strong p 0.01 Evidence against H 0 Very Strong. G: Values below F: the strength of the evidence against the null hypothesis, H 0? a) = none b) = strong c) = very strong d) = moderate : rof., Westchester Community College, NY

9.5 t test: one μ, σ unknown

9.5 t test: one μ, σ unknown GOALS: 1. Recognize the assumptions for a 1 mean t test (srs, nd or large sample size, population stdev. NOT known). 2. Understand that the actual p value (area in the tail past the test statistic) is