Statistics and Hypothesis Testing

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From Hypothesis Testing to Confidence Interval We never learn the true value of µ Y , the population mean of Y (the object inside the box). But from sample data we can specify a range, the confidence interval that is 95 percent (or any other pre-specified percent, the confidence level) likely to include the population mean. Thought experiment: using hypothesis testing, we could exhaustively test the null hypothesis for all possible values of µ Y ,0 and then keep, for the confidence interval, all of those that are not rejected by the data. Since the true value of µ Y will be rejected less than 5 percent of the time, it is 95 percent likely to be on the list.
From Hypothesis Testing to Confidence Interval Practical approach: to construct a 95-percent confidence interval for µ Y from the sample data. All values of µ Y ,0 within 1.96 standard errors of Y will not be rejected. A 95 percent confidence interval for µ Y is Y − 1.96SE(Y ) ≤ µ Y ≤ Y + 1.96SE(Y ) (Reminder: 1.96 corresponds to the 95 percent confidence interval according to the standard normal distribution.)
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 and 26: An example Is the mean wage among r
Page 27 and 28: Average wage example, continued ◮
Page 29: Type I and Type II errors Null Hypo
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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