Question

Shear strength measurements derived from unconfined compression tests for two types of soil gave the results...

Shear strength measurements derived from unconfined compression tests for two types of soil gave the results shown in the following table (measurements in tons per square foot).

Soil Type I Soil Type II

n1 = 30

n2 = 35

y1 = 1.69

y2 = 1.46

s1 = 0.24

s2 = 0.22

Do the soils appear to differ with respect to average shear strength, at the 1% significance level?

State the null and alternative hypotheses.

H0: μ1 = μ2
Ha: μ1 < μ2

H0: μ1 = μ2
Ha: μ1 ≠ μ2    

H0: μ1 ≠ μ2
Ha: μ1 = μ2

H0: μ1 = μ2
Ha: μ1 > μ2

H0: μ1 > μ2
Ha: μ1 = μ2

State the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

z > ___

z < ___

Calculate the appropriate test statistic. (Round your answer to two decimal places. Calculate your test statistic using

y1 − y2.)

z =

What is the conclusion of your test?

Fail to reject H0. There is not enough evidence to conclude the mean shear strength for the two soil types is different.

Reject H0. There is not enough evidence to conclude the mean shear strength for the two soil types is different.    

Fail to reject H0. There is enough evidence to conclude the mean shear strength for the two soil types is different.

Reject H0. There is enough evidence to conclude the mean shear strength for the two soil types is different.

Homework Answers

Answer #1

The statistical software output for this problem is:

Hence,

Hypotheses: Option B is correct.

Rejection region:

z < -2.58

z > 2.58

Test statistic (z) = 4.00

Conclusion: Reject H0. There is enough evidence to conclude the mean shear strength for the two soil types is different.

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