April 16 - We use both tails of the sampling distribution...

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April 16, 2008 Introduction to inferential statistics IV. Testing about a population mean o We can test whether our sample mean is significantly different than a known population mean o Examples: Are college graduates’ salaries different than the overall average salary? Is the average life expectancy for smokers different than the population average? o Based on probability IV. Hypothesis and alpha o Null hypothesis: the sample and population means are equal H 0 : = μ Assuming no difference in age groups (smoking vs. non-smoking) o Alternative hypothesis: they aren’t equal H 1 : μ o Then, select alpha (alpha α=.05) What is the “critical value of z”?: +/- 1.96 Calculating our test statistics: o Formula for calculating z: Z calculated = (- μ)/ (s/ n ) o If z calculated > z critical , we reject the null hypothesis o This means out sample result is unlikely, if H 0 is true IV. Two-tailed test o A non-directional test is called a two-tailed test
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Unformatted text preview: We use both tails of the sampling distribution Our alternative hypothesis is non directional – H : = μ IV. One tailed tests o A directional test is called a one-tailed test We use only one tail of the sampling distribution Out alternative hypothesis is directional – H 1 : > μ IV. Why use a one tailed vs. two-tailed tests? o Only if we have a theoretical reason in advance. o One-tailed test gives us more power o But we might miss unexpected results IV. Using the t-distribution o For smaller samples, we use the t-distribution instead of the z-distribution o Formula is the same: T calculated = (- μ)/ (s/ n ) o But our critical value of t might be different than our critical value of Z Z calc μ = 2.5 Z calculated = (- μ)/ (s/ n ) = 2.8 = (2.8-2.5)/(6/ 100 ) S x = 6 Z calculated = 5 n = 100 α = .05 H : = μ H 1 : ≠ μ...
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