HYPOTHESIS TESTING PROCEDURE STEP 1 Establish the Hypothesis

HYPOTHESIS TESTING PROCEDURE STEP 1. Establish the Hypothesis a. ) Null Hypothesis Ho: b. ) Alternative Hypothesis Ha: = STEP 2. Choose a Significance Level a= STEP 3. Plan the Test a. ) Choose the Test Statistic (formula) b. ) Determine the Rejection Region Z or t 0 F or c 2 0 STEP 4. Collect data and Calculate test statistic STEP 5. Draw conclusion STEP 6. Estimate the parameter of interest and determine Confidence Interval DATA BLOCK

Hypothesis Tests Differences in the Means - Tests for One Population Variance (s 2) known? Yes Test To Use Formula Z - Test x - m 0 s/ n where: x - Sample Mean m 0 - Standard Mean s - Population Standard Deviation n - Sample Size No t - Test Z= t= x - m 0 s/ n where: x - Sample Mean m 0 - Standard Mean s - Sample Standard Deviation n - Sample Size Differences in the Means - Tests for Two Populations – Paired Data Population Variances known? N/A Population Variances Equal? N/A Test to Use Paired Sample t Test Formula d s/ n where : t= d - Sample Differences Mean s - Sample Standard Deviation n - Sample Size

Differences in the Means - Tests for Two Populations Population Variances known? Yes Population Variances Equal? N/A Formula Test to Use Two Pop. Z-Test For Equal Sample Sizes Z= x A - x. B 1 2 (s A + s 2 B ) n where: xi - Sample Mean s i - Population Standard Deviation n - Sample Size For Unequal Sample Sizes Z= x A - x. B s 2 A n. A + s 2 B n. B where: xi - Sample Mean s i - Population Standard Deviation ni - Sample Size No Yes Two – Pop. , Pooled Variance t-Test For equal sample sizes t= x A - x. B s 2 A + s. B 2 n where: xi - Sample Mean si - Sample Standard Deviation n - Sample Size For unequal sample sizes t= x A - x. B æ 1 1 ö SS A + SS B ç + ÷ è n A n. B ø n A + n. B - 2 where: xi - Sample Mean n i - Sample Size

Differences in the Means - Tests for More than Two Populations. Differences in the Dispersion Comparison Population Variance to a Standard Test To Use c 2 - Test Formula c 2 = ( n - 1) s 2 0 where : s - Sample Standard Deviation s - " Standard" or Population Standard Deviation 0 n - Sample Size Two Population Variances F = s A 2 s B 2 F - Test where : s i - Sample Standard Deviation Differences in Proportions Comparison Population Proportion to a Standard Test To Use Z - Test Formula Z= p - P 0 (1 - P 0 ) / n where: p - Sample Proportion n - Sample Size Two Population Proportions Z - Test (2 Pop’s) Z= p 1 - p 2 é 1 1ù p(1 - p)ê + ú ën 1 n 2 û where: pi - Sample Proportion ni - Sample Size x +x p= 1 2 n 1 + n 2 xi - Number of Sample Items with Characteristic of Interest