MS Module 6: Hypothesis testing of proportions (overview 2nd edition)
(The attached PDF file has better formatting.)
(Readings from the second 2nd edition of the Devore text.)
Two complex statistical procedures that are not use in actuarial work (Levene’s test and Tukey’s procedure) have been removed from the syllabus, simplifying modules 10-14 on analysis of variance (ANOVA). To keep the 24 module sequence,
● Module 4 Hypotheses and Test Procedures is now split into
○ Module 4a Type 1 and Type 2 errors:
○ Module 4b Tests about a population mean
● Module 5 Hypothesis testing of proportions is now split into
○ Module 5a Tests About a Population Proportion
○ Module 5b Hypothesis testing – p values
Reading: §9.3: Tests About a Population Proportion
● Large sample tests use the central limit theorem and an approximate normal distribution.
● Small sample tests use the binomial distribution.
Know the test statistic value of z for large sample tests. Review §3.5 if you are not familiar with the binomial distribution. Example 9.11 shows the seven step procedure.
If the null hypothesis is not true, the Z statistic is still normally distributed but its mean and variance are not 0 and 1. The β values (probabilities of Type II errors) depend on the type of null hypothesis (one-tailed or two-tailed) and the value of p0 and pʹ (the proportions in the null hypothesis and the assumed alternative).
For two-sided null hypotheses, we use the absolute value of pʹ – p0. For a one-side (single tailed) null hypothesis, check whether pʹ is larger or smaller than p0 before plugging values into the formula. If pʹ is in the null hypothesis, computing β makes no sense.
The equations right above Example 9.12 seem complex, but they all use the same adjustment to previous equations. The formulas use the additional parameters √(pʹqʹ) and √(p0q0). Know Example 9.12 (large sample) and Example 9.13 (small sample), on which final exam problems may be modeled.
Review end of chapter exercises 36, 37, 38, 39, 40, and 41.
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