Stat5601 Midterm

Stat5601 Midterm - Midterm 1 STAT 5601 Fall 2010 This paper contains 40 points Show the details of your calculations for full credit Name SID

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Midterm 1 STAT 5601 Fall 2010 This paper contains 40 points. Show the details of your calculations for full credit. Name: SID: Consider the following data: 7 , 10 , 6 , 6 , 3 , 10 , 19 . 1. Obtain the empirical distribution function (edf) based on the above data. You may either present it as a probability mass function or cumu- lative distribution function in a table, or draw a plot of the cumulative distribution function. [10 points] 2. Find the vectors of rank and order statistics from the above data. [5 points] 3. What is the median in this data? [2 points] 1
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4. Find the trimmed mean μ LTS ) from the above data that achieves 20% breakdown value. Justify your answer in one or two sentences. [8 points] 5. Assume that the above data is an i.i.d. sample from a continuous dis- tribution F which has median ( F ) = θ . We want to test the null hypothesis H 0 : θ = 5 against the alternative H 1 : θ n = 5. Obtain the values of the signed rank test statistic and the sign test statistic for the above test. [Hint: First subtract the value of θ under the null hypothesis from each observation.] The formula for both test statistics are given at the end of this exam paper. [10 points]
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This note was uploaded on 02/24/2011 for the course STAT 5601 taught by Professor Staff during the Fall '06 term at Minnesota.

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Stat5601 Midterm - Midterm 1 STAT 5601 Fall 2010 This paper contains 40 points Show the details of your calculations for full credit Name SID

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