Question

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).

Soil Type 1 Soil Type 2 n1 = 31 n2 = 35 x1 = 1.56 x2 = 1.47 s1 = 0.24 s2 = 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

Answer:-

Given that:-

a)To test the hypothesis is that the soils do appear to differ with respect to mean shear strength at 5% significance level. The type of test is two - samples t- test assumes equal standard deviations are used due to the standard deviation of two types of soils are nearer.

The null and alternavtive hypothesis is,

The t-test statistics is,

First ,compute pooled variance then find test statistics.

The pooled variance is,

The t - test statistics is,

The t -test statistics is 1.625.

The t - critical value is,

The sample size is small and two -tailed test .Look in the column headed and the row headed in the t distribution table by using degree of freedom is,

The t - critical value is -1.998 and 1.998

Decision

The conclusion is that the t - test statistics which us 1.625 is less than t- critical value which is 1.998 , so the null hypothesis is not rejected at 5% level of significance . There is insufficient evidence to indicate that the soils do appear to differ with respect to mean strength. The result is not statistically siginificant.

b)A 95% confidence interval on the mean shear strength difference between two types of soils is,

95% C.I

to

A 95% confidence interval on the mean shear difference between two types of soils is -0.02 to 0.02

This confidence interval does come to the same conclusion as results in part (a) due to a 95% confidence interval on the mean sgear strength difference between two types of soils is between -0.02 and 0.20 does include 0 indicate that there is insufficient evidence to indicate that the soils do appear to differ with respect to mean shear strength.