Statistics and Hypothesis Testing

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Hypothesis Testing With statistical methods, we can test hypotheses about population parameters, e.g., the population mean. For example: Does the population mean of hour earnings equal $20 per hour ◮ Define the null hypothesis H 0 : E(Y ) = µ Y ,0 H 0 : E(hourly earnings) = $20 per hour ◮ Define the alternative hypothesis. H 1 : E(Y ) ≠ µ Y ,0 H 1 : E(hourly earnings) ≠ $20 per hour ◮ Gather a sample of data and compute the actual sample mean
Hypothesis Testing 1. Gather a sample of data and compute the actual sample mean 2. If the null hypothesis were true, would the r.v. the sample mean likely be as big (or small) as the actual sample mean [ ∣∣Y ∣ ∣ ∣] Pr − µY ,0 ∣∣Y act ∣∣ > − µY ,0 H 0 (There is only one random variable in the preceding mathematical phrase. Can you find it) 2.1 If so (the probability is large), “accept the null hypothesis” (which does not mean that the null hypothesis is true, simply that the data do not reject it). 2.2 If not (the probability is small), “reject the null hypothesis” in favor of the alternative.
Page 1 and 2: Statistics and Hypothesis Testing M
Page 3 and 4: Summary of Main Points ◮ We will
Page 5 and 6: What would be a good way to guess
Page 7 and 8: Y is the least squares estimator of
Page 9: Random Sampling The consequences of
Page 13 and 14: The p-Value p-value ≡ Pr H 0 [
Page 15 and 16: How likely is the observed value In
Page 17 and 18: Sample Variance, Sample Standard De
Page 19 and 20: Sample Standard Deviation The sampl
Page 21 and 22: Summary: Why standard error ◮ Can
Page 23 and 24: The Prespecified Significance Level
Page 25 and 26: An example Is the mean wage among r
Page 27 and 28: Average wage example, continued ◮
Page 29 and 30: Type I and Type II errors Null Hypo
Page 31 and 32: From Hypothesis Testing to Confiden
Page 33 and 34: Example: 95 percent CI In a sample
Page 35: Next time we do something from the

Statistics and Hypothesis Testing

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