Week_9_Practice_Problems

Week_9_Practice_Problems - Week 9 Practice Problems These...

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Week 9 Practice Problems These problems all use the t distribution for tests of significance in Gaussian response models. 1. A measurement system is tested by repeatedly measuring a known standard with certified known value 1.000 cm. The data are 1.03, 1.04, 1.02, 0.99, 1.02, 1.00 Consider the model , ~ (0, ), 1,. ..,6 independent ii i YR R G i μ σ =+ = a) What would it mean about the measurement system if 1 > ? b) Is there any evidence that differs from 1? [Your answer should show all 5 steps of a test of significance] c) Find a 95% confidence interval for . Is 0 = in the confidence interval? 2. Suppose we have data 1 ,..., n y y and the model xx , ~ (0, ), 1,. .., independent i R G in = with ˆˆ 10.7, 1.77 == . We are interested in assessing if there is any evidence that differs from 10. a) Calculate the p-value for testing the hypothesis 10 = if and 30. 10,20 n = b) What happens to the strength of evidence against the hypothesis as n increases? 3. Suppose we have the following data on a response and explanatory variates x y x y 2.95 4.51 2.24 4.24 1.44 3.56 5.28 3.66 2.08 4.76 0.54 4.52 1.92 3.11 4.33 4.15 1.15 3.28 0.47 4.29 4.28 5.47 0.53 3.33 1.31 4.22 1.88 3.30 4.86 4.28 1.72 3.43 6.43 5.06 0.22 2.93
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This note was uploaded on 03/20/2011 for the course STATISTICS 231 taught by Professor Mckay during the Spring '10 term at Waterloo.

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Week_9_Practice_Problems - Week 9 Practice Problems These...

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