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 –Identify population of interest and parameter –State H 0 and H a 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

tαtα -t α/2 t α/2 -t α Critical Region x – μ 0 Test Statistic: t 0 = s/√n Reject null hypothesis, if P-value < α Left-TailedTwo-TailedRight-Tailed t 0 < - t α t 0 < - t α/2 or t 0 > t α/2 t 0 > t α P-Value is the area highlighted |t 0 |-|t 0 | t0t0 t0t0

Reject null hypothesis, if μ 0 is not in the confidence interval Confidence Interval: x – t α/2 · s/√n x + t α/2 · s/√n Confidence Interval Approach Lower Bound Upper Bound μ0μ0 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 x diff – μ 0 t 0 = s diff / √n

zαzα -z α/2 z α/2 -z α Critical Region Reject null hypothesis, if P-value < α Left-TailedTwo-TailedRight-Tailed z 0 < - z α z 0 < - z α/2 or z 0 > z α/2 z 0 > z α P-Value is the area highlighted |z 0 |-|z 0 | z0z0 z0z0 p – p 0 Test Statistic: z 0 = p 0 (1 – p 0 ) n

Reject null hypothesis, if p 0 is not in the confidence interval Confidence Interval Approach Lower Bound Upper Bound p0p0 P-value associated with lower bound must be doubled! Confidence Interval: p – z α/2 ·√(p(1-p)/n p + z α/2 · √(p(1-p)/n << << <<

Are you prepared for the Test?

Summary and Homework Summary –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; to x – μ 0 t 0 = s / √n p – p 0 z 0 = p 0 (1 – p 0 ) n