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# ass2sol - Stat 231 Assignment 2 Solutions 1 To certify its...

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Stat 231 Assignment 2 Solutions 1. To certify its measurement system for determining the cholesterol level in blood serum, a medical laboratory uses the following Plan one day each year. Collect 40 tubes of serum, labeled T1,…,T40, from some of the patients entering the laboratory in a single day. Choose the patients so the cholesterol levels vary over the range 120 to 400 mg/dL, the range expected in normal use. This is possible because many patients are repeat customers. Split the contents of each tube Ti into two vials labeled Ti1 and Ti2 ( 1,...,40 i = ). Ship the set of vials with label ending in 1 to a nationally certified laboratory. Measure two vials with label ending in 2 every hour over 20 hours. Record each cholesterol level, the time of measurement and the operator making the measurement. Once the data have been received from the nationally certified laboratory, enter the two measured values for each tube into a spreadsheet for analysis. The laboratory management wanted to assess the bias and variability of the measurement system. They assumed that the values from the nationally certified laboratory were close to the true values. Problem A unit is the act of measuring the serum cholesterol level on a vial and the target population is all such acts in the upcoming year. The response variate is the measured level of cholesterol in the vial. a) Using suitable notation, write symbolic expressions for the attributes of interest. Define all symbols. Let e i be the measurement error, the difference between the measured and true value for the ith act of measurement in the target population. Suppose there are N such acts. Then the attributes of interest are the average and standard deviation of the measurement errors in the target population P which can be written symbolically as e e N i i P = ° ε , 2 ( ) 1 i i P e e N ε - - ° b) State the Problem in terms of these attributes. The laboratory wanted to estimate these two attributes. The laboratory also wanted to be sure that the bias and variability of the measurement system were not influenced by the true level of the cholesterol or the operator. Plan c) What was a study unit? What was the study population? A study unit is the act of measuring the serum cholesterol level on a vial and the study population is all such acts possible in the day of the investigation. d) What explanatory variates were measured? Why were these variates measured?

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