Question

by using median based on wilcoxon signed-ranks test

2.9 Hall et al. (E13) computed the ratio of Lintner Soluble Starch (LSS) to Amylase Azure (AA) values (enzyme units per milliliter) determined from saliva specimens from 11 sub- jects. The results are shown in Table 2.15, Obtain a point estimate, and construct an approximate 95% confidence interval for the median of the population of similar subjects from which these subjects may be considered a random sample. Ratio of Lintner Soluble Starch (LSS) to Amylase Azure (AA), enzyme units per milliliter K 0:86 Subject A D E F G H 0.78 (0,65 0.85 0,64 0.70 0.86 0.82 Ratio LSS/AA 1.10 1,00 Source: F. F. Hall, C. R. Ratliff, T. Hayakawa, T. W. Culp, and N. C. Hightower, "Substrate Differentiation of Human Pancreatic and Salivary Alpha-Amylases,' Am. J. Dig. Dis., 15 (1970), 1031-1038.

Answer 1

95% confidence interval for the median of the population of similar subjects from which these subjects may be considered a random sample is

Median: Observations in the ascending order are: 0.64, 0.65, 0.7,0.71, 0.78, 0.82, 0.85,0.86, 0.86, 1, 1.1 Here, n 11 is odd. n1t M= value of observation th observation value of 2 = value of 6 observation 0.82

From the given data

fix =($D$3+F2)/2 F3 A C D E G H J K L M O P 1 X-37 Samples(X) 0.28 0.17 0.03 0.12 2 S.No. X-0.82 0.04 0,04 0 0.11 0.18 0.18 0.04 -0.04 0.02 0.16 0.105 1 0.78 0.04 0.04 0.04 0.075 0.11 0.035 0.11 0.04 0.08 4 2 0.86 0.04 0.04 0.04 0.03 0.1 0.0575 0.075 0.0725 0.0375 0.075 0.04 0.06 0.09 0.02 5 3 0.82 0 0 0 0.14 0.055 0.09 0.085 0.015 0.06 6 4 1.1 0.28 0.28 0.28 0.195 0.23 0.225 0.155 0.23 0.16 0.2 -0.11 0.11 7 5 0.71 0.145 0.18 0.175 0.105 0.18 0.11 0.15 0.15 8 6 1 0.18 0.18 0.18 0.175 0.105 0.18 0.11 -0.17 9 7 0.65 0.17 0.17 0.1 0.175 0.105 0.145 0.85 0.03 10 8 0.03 0.03 0.105 0.035 0.075 0.64 0.18 0.11 0.15 11 9 -0.18 0.18 12 10 0.86 0.04 0.04 0.04 0.08 -0.12 0.12 13 11 0.7 0.12 14 11 COUNT(A3:A13) 15 n = 16 alpha 17 0.05 10 from the signed rank test 18 T crit 19 Median 0.105 MEDIAN(F3:P13) 20 21 T Crit 11 0.04 SMALL(F3:P13,C21) 22 Lower 0.18 LARGE(F3:P13, C21) 23 Upper 24 25 Sheet1 Sheet2 Sheet3 Ready

The 95% confidence interval is (0.04, 0.18)