HYPOTHESIS TESTING

INTRODUCTION

STATISTICAL INFERENCE

  • Make inferences, and do CONCLUSION about the population

How do make conclusion?

  • Estimate population parameter by calculate the MEAN of population
  • Develop HYPOTHESIS TESTING

HYPOTHESIS TESTING

  • Involve drawing inferences 2 CONTRASTING PROPOSITIONS to the value 1/more population
  • NULL HYPOTHESIS (describing existing and current situation)
  • ALTERNATIVE HYPOTHESIS (Complement H0)

Reject H0, if provide sufficient EVIDENCE to support H1

STEPS IN CONDUCT HYPO TEST

  1. IDENTIFY the population parameter and formulate the hypotheses to test.
    1. Select a LEVEL of SIGNIFICANT (the risk of drawing an incorrect conclusion)
  2. DETERMINE the DECISION rule on which to base a conclusion
  3. COLLECT DATA and CALCULATE a TEST STATISTIC
    5.Apply the decision rule and DRAW a CONCLUSION.

THREE TYPES OF ONE SAMPLE TESTS

  1. H0: parameter ≤ constant H1: parameter > constant
  2. H0: parameter ≥ constant H1: parameter < constant
  3. H0: parameter = constant H1: parameter ≠ constant
  • It is NOT CORRECT to formulate a NULL hypothesis using >, <, or ≠.

POTENTIAL ERRORS

  1. H0 is TRUE and the test correctly FAILS to reject H0
  2. H0 is FALSE and the test CORRECTLY reject H0
  3. H0 is TRUE and the test CORRECTLY rejects H0 (called Type I error)
  4. H0 is FALSE and the test FAILS to reject H0 (called Type II error)

TERMINOLOGY

Alpha (level of SIGNIFICANT) - TYPE I error

  • 1- alpha called CONFIDENCE COEFFICIENT

TYPE II error - Beta

  • 1-beta called POWER OF THE TEST

α decreases, β increases

The power of the test can be increased by taking larger samples, which enable us to detect small differences between the sample statistics and population parameters with more accuracy

TEST STATISTIC

  • Z TEST - SD KNOWN
  • T TEST - SD UNKNOWN

DRAW A CONCLUSION

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