Question 6 Background Identification of Criminals... Continued In the second iss

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Question 6 Background Identification of Criminals... Continued In the second issue of Biometrika, W. R. Macdonell (1902) published an extensive paper, On Criminal Anthropometry and the Identification of Criminals in which he included numerous tables of physical characteristics 3000 non-habitual male criminals serving their sentences in England and Wales. His Table ll (p. 216) recorded a bivariate frequency distribution of height by finger length. His main purpose was to show that Scotland Yard could have indexed their material more efficiently, and find a given profile more quickly W. S. Gosset (aka "Student") used these data in two classic papers in 1908, in which he derived various characteristics of the sampling distributions of the mean, standard deviation and Pearson's r. He said, "Before l had succeeded in solving my problem analytically, l had endeavoured to do so empirically." Among his experiments, he randomly shuffled the 3000 observations from Macdonell's table, and then grouped them into samples of size 4, 8, calculating the sample means, standard deviations and correlations for each sample. Question 6 Subquestions 6.a Fill in the black: The 99% prediction interval for the Finger Length would be then the 99% confidence interval for the expected Finger Length. (Select one.) point(s) Narrower Wider About the same width 6.b For which value of the Height would you expect the 99% prediction interval for the Finger Length to be the narrowest? (Select one) point(s) These numerical summaries may help: mean sd 0% 25% 50% 75% 100% Finger Length 11.55 0.55 9.50 11.20 11.50 11. 90 13.50 3000 Height 5.42 0.21 4.63 5.30 5.38 5.55 6.38 3000 4.72 decimal ft 5.39 decimal ft 5.82 decimal ft

Explanation / Answer

(A) A prediction interval is always wider than confidence interval so a 99% prediction intervel is wider than 99% confidence interval.

So, OPtion B is corect.

(B) The formula for prediction interval so at x = xn+1 for y = yn+1

= > yn+1 +- t/2, n-2 sqrt (MSE) sqrt [ 1 + 1/n + (xn+1 - xbar)2/ (xi -x )2 ]

so the range of prediction interval is directly proportional to (xn+1 - xbar)

so for the given 3 values x = 5.39 decimal ft has lowest values of (xn+1 - xbar) so it would have lowest width among these 3.

Q.6 (c) Option (1) is true that samle residuls have a nomral model.

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