Hypothesis Testing

Definitions

Alternative Hypothesis: (a.k.a. H₁) a statement (about a population parameter) that is contrary to the null hypothesis. Usually this is what a researcher is trying to prove.

Confidence Coefficient: the probability of not rejecting H₀ when it is true.

Critical Value: a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.

H₀: See Null Hypothesis.

H₁: See Alternative Hypothesis.

Hypothesis Testing: the formal procedures used by statisticians to accept or reject statistical hypotheses.

Level of Significance: the probability of rejecting the null hypothesis when it is true, i.e. probability of committing Type I Error.

Null Hypothesis: a claim whose validity is tested. Usually this is what a researcher is trying to disprove.

p-Value: the probability of obtaining a sample statistic equal to or "more extreme" than what was actually observed, when the null hypothesis is true.

Power of a Statistical Test: the probability that the test correctly rejects the null hypothesis when the alternative hypothesis is true.

t_STAT: a test statistic when the population standard deviation σ is not known.

Test Statistic: standardized value of a sample statistic.

Type I Error: the (incorrect) rejection of a true null hypothesis.

Type II Error: the failure to reject a false null hypothesis.

Z_STAT: a test statistic when the population standard deviation σ is known.

Read These

Chapter 9. Fundamentals of Hypothesis Testing: One-Sample Tests in the textbook:

9.1 Fundamentals of Hypothesis Testing Methodology (pp. 309-320)

9.2 t Test of Hypothesis for the Mean (σ Unknown) (pp. 321-325)

You may omit section 9.3 One-Tail Tests (pp. 328-331)

9.4 Z Test of Hypothesis for the Proportion (pp. 332-335)

You may omit section 9.5 Potential Hypothesis-Testing Pitfall and Ethical Issues (pp. 336-337)

You may omit section 9.6 Power of a Test (pp. 337-338)

Watch This

Hypothesis Testing. This is the list of 16 videos discussing the concepts and and the practical advice to test a hypothesis. You may want to review all of them or just those that you feel you have difficulties with.

Answer These

Do problem 9.71 (p. 340 in the textbook).

Do problem 9.72 (p. 340 in the textbook).