One-Sided Hypothesis Testing and Proportions in Statistics, Exams of Statistics

Download One-Sided Hypothesis Testing and Proportions in Statistics and more Exams Statistics in PDF only on Docsity! Stat 371 Spring 2005 Mar. 14, 2005 Discussion 8 1 One-Sided Test Suppose Y1, ..., Yn have the normal distribution, N (µ, σ2). H0 : µ ≤ µ0 versus HA : µ > µ0 H0 : µ ≥ µ0 versus HA : µ < µ0 Test statistics: z = ȳ − µ0 σ/ √ n or t = ȳ − µ0 s/ √ n Situation HA Reject H0 Note σ known µ > µ0 z > zα µ < µ0 z < −zα σ unknown µ > µ0 t > tn−1,α µ < µ0 t < −tn−1,α n large µ > µ0 z > zα Replace σ with s µ < µ0 z < −zα Replace σ with s 1.1 Example E. canis infection is a tick-borne disease of dogs that is sometimes contracted by humans. Among infected humans, the distribution of white blood cell counts has an unknown mean µ and a standard deviation σ. In the general population, the mean white blood cell count is 7250/mm3. It is believed that persons infected with E. canis must on average have lower white blood cell counts. (a) What are the null and alternative hypotheses for a one-sided test? (b) For a sample of 15 infected persons, the mean white blood cell count is ȳ = 4767/mm3 and the standard deviation is s = 3204/mm3. Conduct the test at the α = 0.05 level. (c) What do you conclude? 1250D MSC ting-li@stat.wisc.edu Ting-Li Lin