By William Feller
Significant alterations during this variation contain the substitution of probabilistic arguments for combinatorial artifices, and the addition of recent sections on branching methods, Markov chains, and the De Moivre-Laplace theorem.
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Extra resources for An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition
The research hypothesis is HA: There is a difference between the observed distribution of survey scores and a normally distributed empirical sample. 05. 05 in our example. In other words, there is a 95% chance that any observed statistical difference will be real and not due to chance. 3 Choose the Appropriate Test Statistic We are seeking to compare our observed sample against a normally distributed empirical sample. The Kolmogorov–Smirnov one-sample test will provide this comparison. 4 Compute the Test Statistic First, determine the midpoint and standard deviation for the observed sample.
5. 3 in Appendix B, which lists the critical values for the Wilcoxon T. 2, the two counselors with score differences of zero were discarded. This reduces our sample size to n = 10. 05. 3 returns a critical value for the Wilcoxon test of T = 8. An obtained value that is less than or equal to 8 will lead us to reject our null hypothesis. 5. If the critical value equals or exceeds the obtained value, we must reject the null hypothesis. If instead, the critical value is less than the obtained value, we must not reject the null hypothesis.
05. 05 in our example. In other words, there is a 95% chance that any observed statistical difference will be real and not due to chance. 3 Choose the Appropriate Test Statistic The data are obtained from 25 counselors, or participants, who are using a new program designed to reduce bullying among students in the elementary schools. The participants reported the percentage of successful interventions last year and the percentage this year. We are comparing last year’s percentages with this year’s percentages.
An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition by William Feller