ams572_notes_4

ams572_notes_4 - AMS 572 Lecture Notes #M Sept. 20, 2010....

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AMS 572 Lecture Notes # M Sept. 20 , 2010. One-sample Inference on Population Mean When the population i s normal, and the population variance known Data : Any population, the population variance is unknown However – the sample size is large Normal Population, but the variance is unknown 100 years ago – people used Z-test This is OK for n large CLT (** although the exact t-test is better because it is exact **) This is NOT OK if the sample size is samll. 1
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“A Student of Statistics” – pen name of William Sealy Gosset (June 13, 1876–October 16, 1937) http://en.wikipedia.org/wiki/William_Sealy_Gosset “The Student’s t-test” P.Q. (Exact t-distribution with n-1 degrees of freedom ) Wrong Test for a 2-sided alternative hypothesis 2
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Right Test for a 2-sided alternative hypothesis Reject *Even if the sample size is large, if the population is normal, the t-test is the exact test 0 and thus better than the large sample approximate Z-test based on CLT. (Because t distribution has heavier tails than normal distribution.)
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ams572_notes_4 - AMS 572 Lecture Notes #M Sept. 20, 2010....

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