Statistics and Hypothesis Testing

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Defining “too much.” We know that under the null hypothesis, the sample mean is a random variable distributed in a particular way: N(µ Y ,0 , σ 2 Y ). Because this is a normal distribution, we know exactly the probability that the sample mean is more than any specified distance away from the hypothesized mean (if the hypothesized mean is accurate). For example, it is less than 5 percent likely that the sample mean will be more than 2 (really 1.96) standard deviations away from the hypothesized mean (if the hypothesized mean is accurate).
How likely is the observed value In words, the p-value is how likely the random variable Y is to exceed the observed actual Y act if the null hypothesis is true. As p falls, we become increasingly sure that the null hypothesis is not true. (It’s really unlikely that we could have a sample mean this big (small) if the null were true. We do have a sample mean this big (small). Ergo, the null hypothesis is not true.) Convert to a standard normal problem
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: The p-Value p-value ≡ Pr H 0 [
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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