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## Ch. 26 Tests of significance

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**Ch. 26 Tests of significance**• Example: • Goal: Decide if a die is fair. • Procedure: Roll a die 100 times and count the number of dots. We observe 368 total dots in 100 rolls. • Chance model: If the die is fair, Box model Average SD of box EVsum SEsum**So we expect the total (sum of dots) to be around 350 give**or take 17, or so. • What is the chance of observing a total of 368? z= The chance of getting results as extreme as 368 (or more) is**Same situation by 1000 rolls and observe a total of 3680.**• Language: • Null hypothesis: Assume a specific chance process is at work (box model). • Alternative hypothesis: Another statement about the box. • Test statistic: Measures the difference between what is observed in the data and what is expected based on the null hypothesis.**In our example,**• Null hypothesis: The die is fair. • Alternative hypothesis: The die is “loaded” so as to favor higher numbers. • P-value of a test = significance level • Probability/chance of getting a test statistic as extreme as, or more extreme than, the one based on observation.**Probability of observed result assuming the null hypothesis**is true. (Not the probability that the alternative hypothesis is true.) • High p-value gives evidence supporting the null hypothesis. • Low p-value gives evidence against the null hypothesis. • Using z is appropriate for “large” samples and when the probability histogram is approximately normal.**Exercise C #7 p. 483**• A results is said to be statistically significant if the p-value is less than 5% and highly significant if the p-value is less than 1%.