Week_6_Practice_Problems_Solutions

# Week_6_Practice_Problems_Solutions - Week 6 Practice...

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Unformatted text preview: Week 6 Practice Problems 1. (using the 2 χ and t tables) Find the following a) a constant c so that 2 30 ( ) 0.975 P c χ > = c=16.791 b) a constant c so that 2 20 ( ) 0.975 P c χ > = c=9.591 c) constants so that 1 2 , c c 2 1 1 2 ( ) P c c χ < < = . 9 5 1 2 3.247, 20.483 c c = = (there are many other answers) d) Repeat a) to c) with 2 χ replaced by student’s t . a) c=-2.0423 b) c=-2.0860 c) (there are many other answers) 1 2 2.2281, 2.2281 c c = − = e) estimate 2 15 ( 2 P χ > 5 ) p=0.05 f) estimate 6 (| | 2) P t > p=0.045 2. In a pilot study to test a complex questionnaire to be used in a large survey, 10 volunteers agreed to be surveyed. A key response variate was a score based on the answers to 25 different questions. The data are shown below with some summaries. average stdev score 57.6 58.3 56.4 57.4 56.1 58.3 49.9 55.6 51.8 56.1 55.74 2.78 The researchers decided to model the data using a simple Gaussian response model 1 1 , ,..., ~ (0, ) independent i i Y R R R G μ σ = + a) What do the parameters μ and σ represent? μ represent the mean of the score and σ represent the standard deviation of the scores in the study population....
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Week_6_Practice_Problems_Solutions - Week 6 Practice...

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