Statistics and Hypothesis Testing

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Average wage example, continued The sample standard deviation is s Y = $18.14. ◮ Compute the standard error of Y SE(Y ) = s Y / √ n = 18.14/ √ 200 = 1.28 ◮ Compute the t-statistic t = Y act − µ Y ,0 SE(Y ) 22.64 − 20 = 1.28 = 2.06 Now how likely is it that our sample would generate a t-statistic of 2.06 when we would expect a t-statistic of zero under the null hypothesis
Average wage example, continued ◮ Compute the p-value p = 2Φ(−|t|) = 2Φ(−2.06) = 2(0.0197) = 0.039, or 3.9 percent Conclusion: it is fairly unlikely that the mean earnings among recent college graduates is $20 per hour given that our sample of 200 had mean earnings of $22.64 (and standard deviation of $18.14). If we were using the conventional significance level of 5 percent, we would reject the null hypothesis.
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 and 10: Random Sampling The consequences of
Page 11 and 12: Hypothesis Testing 1. Gather a samp
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: An example Is the mean wage among r
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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