Question

3. Shear strength measurements derived from unconfined compression tests for two types of soils gave the results shown in the following table (measured in tons per square foot). Math 1P98 Spring 2020 Assignment #2 Due Friday, June 26, 2020 Soil Type 1 Soil Type 2 ni = 31 n2 = 35 21 = 1.56 T2 = 1.47 81 = 0.24 82 = 0.21 (a) Do the soils appear to differ with respect to mean shear strength? Use the critical value method at the 5% significance level. (b) Create a 95% confidence interval on the mean difference. Does this confidence interval come to the same conclusion as your result in part a)?

Answer 1

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Ik taje I Null heses, Hos Mially There is not significant difference Setween mean theai stogte of two types of soil. Alternative hypothesis H, : 4,7 M There is significant difference between shengen of two types of soil. Test statistic 60 mean shear 360 n = 31 a = 1.56 si - 0-24 11, ł n =35 no = 1.47 wosz = 0.21 t where s=/6,-1) 87 m ² nifat th ni no

Page 2 O Date Go Page No. 30 (0.24) ²+ 34 (0.21) 2 31+35-2 O. 04 7461765 dr 0.217857 0.2178 1-56 - 1.47 31 0-2178 ttt 35 t=1.62498 t 00025164 Level of significance ES Two talled test. de f. = nith -2- 31+35-2=64 Cretical value = 1.997 Calculated value < Critical value we fail fail to reject the null hypothesis the soil do not appear to differ wer-t mean shear strength Nol

Date: ............... Page No. : + ffo.o25,64) 3135 Page 3 b) 95% confidence interval on mean difference [x - 7) + trooss, nared) Afth the (1-56 -1.47 0-273/ 10.09) + 1.997x 0.2178 X. 1 t tt 0.09 I 0.1106 957.C → (-0.0206, 0.2006 Since the interval includes zero. it means null hypothesis is true. lie confidence interval gines the conclusion my result in part (a). 31 35 6 ) so as same