Week_6_Practice_Problems

# Week_6_Practice_Problems - Week 6 Practice Problems 1(using...

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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 Pc >= b) a constant c so that 2 20 ( ) 0.975 c) constants so that 12 , cc 2 11 02 () c <<= 0 . 9 5 d) Repeat a) to c) with 2 replaced by student’s t . e) estimate 2 15 (2 P > 5 ) f) estimate 6 (| | 2) Pt > 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 0 , ,..., ~ (0, ) independent ii YR R R G μ σ =+ a) What do the parameters and represent? b) What are the estimates of and ? c) What are the distributions of the corresponding estimators? d) Find a 90% confidence interval for and . e) Provide an informal and a formal interpretation for the CI for 3. The form of a 95% CI for is ˆˆ (,) ab where a and b are chosen based on the confidence level. We can think of

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Week_6_Practice_Problems - Week 6 Practice Problems 1(using...

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