103lect2hand

103lect2hand - Hypothesis Testing - I Recall that we have...

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Hypothesis Testing - I • Recall that we have an estimator, Y , of μ Y . • While this estimator is unbiased and consistent , Y will generally not be exactly equal to μ Y . This is because we only used a sample of size n . Our sample may have somewhat high Y i ’s (in which case Y will be greater than μ Y ) or somewhat low Y i ’s (in which case Y will be less than μ Y ) Hypothesis Testing - II • Suppose we want to formally "test” whether μ Y equals a specific number, e.g. we want to test the hypothesis that the mean wage in the US is 80 (thousand dollars), i.e. whether μ Y =80. • Suppose that you collect a random sample, and suppose that Y = 84 (thousand dollars). Should you “reject” your hypothesis? • The problem is that even if μ Y does actually equal 80, it is possible that Y might equal 84 due to the randomness in the sample. Hypothesis Testing - III • Hypothesis testing takes this possibility into account and tells us whether, based on statistical evidence, we should “reject” our hypothesis. • Caveat: Hypothesis testing is still not 100%. Due to randomness in the sample, there is always the possibility that we will come to the wrong conclusion. However, we can measure and control this possibility and try to make it small.
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Hypothesis Testing - IV • To formally do a hypothesis test, we set up the test in terms of a “null hypothesis” (H 0 ) and an “alternative hypothesis” (H A ) • In our example, the test is: H 0 : μ Y = 80 vs. H A : μ Y 80 Hypothesis Testing - V • There are two possible statistical conclusions of this hypothesis test: – 1) “Reject H 0 – 2) “Don’t reject H 0 • If we “Reject H 0 ”, we are saying that there is statistical evidence that H 0 is false and that H A is true.
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103lect2hand - Hypothesis Testing - I Recall that we have...

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