Review of Chapter 12 Significance Tests in Practice Lesson 12 - R Review of Chapter 12 Significance Tests in Practice

Objectives Conduct one-sample and paired data t significance tests. Explain the differences between the one-sample confidence interval for a population proportion and the one-sample significance test for a population proportion. Conduct a significance test for a population proportion.

Vocabulary None new

Inference Toolbox Step 1: Hypothesis Step 2: Conditions Identify population of interest and parameter State H0 and Ha Step 2: Conditions Check appropriate conditions Step 3: Calculations State test or test statistic Use calculator to calculate test statistic and p-value Step 4: Interpretation Interpret the p-value (fail-to-reject or reject) Don’t forget 3 C’s: conclusion, connection and context

Reject null hypothesis, if P-Value is the area highlighted -tα -tα/2 tα/2 tα t0 -|t0| |t0| t0 Critical Region x – μ0 Test Statistic: t0 = ------------- s/√n Reject null hypothesis, if P-value < α Left-Tailed Two-Tailed Right-Tailed t0 < - tα t0 < - tα/2 or t0 > tα/2 t0 > tα

Confidence Interval Approach x – tα/2 · s/√n x + tα/2 · s/√n Lower Bound Upper Bound μ0 Reject null hypothesis, if μ0 is not in the confidence interval P-value associated with lower bound must be doubled!

Using t-Test on Differences What happens if we have a match pair experiment? Use the difference data as the sample Use student-t test statistic With previously learned methods xdiff – μ0 t0 = -------------- sdiff / √n

Reject null hypothesis, if P-Value is the area highlighted -zα -zα/2 zα/2 zα z0 -|z0| |z0| z0 Critical Region p – p0 Test Statistic: z0 = -------------------- p0 (1 – p0) n Reject null hypothesis, if P-value < α Left-Tailed Two-Tailed Right-Tailed z0 < - zα z0 < - zα/2 or z0 > zα/2 z0 > zα

Confidence Interval Approach p – zα/2 ·√(p(1-p)/n p + zα/2 · √(p(1-p)/n < Lower Bound Upper Bound p0 Reject null hypothesis, if p0 is not in the confidence interval P-value associated with lower bound must be doubled!

Are you prepared for the Test?

Summary and Homework Summary Homework Remember the 4 steps of the Inference Toolbox Three conditions for inference testing: SRS, Normality, and Independence Test statistic format the same Homework pg 775 – 77; 12.31 to 12.38 p – p0 z0 = ------------------- p0 (1 – p0) n x – μ0 t0 = -------------- s / √n