The Grubbs' test, which is described by Algorithm 10.1, is a more statistically sophisticated procedure for detecting outliers than that of Definition 10.3. It is iterative and also takes into account the fact that the z-score does not have a normal distribution. This algorithm computes the z-score of each value based on the sample mean and standard deviation of the current set of values. The value with the largest magnitude z-score is discarded if its z-score is larger than gc, the critical value of the test for an outlier at significance level α. This process is repeated until no objects are eliminated. Note that the sample mean, standard deviation, and gc are updated at each iteration.

(a) What is the limit of the value

used for Grubbs' test as m approaches infinity? Use a significance level of 0.05.
(b) Describe, in words, the meaning of the previous result.

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Algorithm 10.1 Grubbs' approach for outlier elimination 1: Input the values and α (m is the number of values, a s a parameter, and tc s a value chosen so that a = prob(r-te) for a t distribution with Tn-2 degrees of freedom.) 2: repeat 3: Compute the sample mean T) and standard deviation (s) 4: Compute a value ge so that problea (In terms of te and m, 5: Compute the z-score of each value, i.e., z(r-T)/S e., find the z-score of largest magnitude and call it g 7: if g> ge then 8 Eliminate the value corresponding to g 9: 10: end if 1 until No objects are eliminated m-2+t