Question

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
H_a: μ₁ < μ₂

H₀: μ₁ = μ₂
H_a: μ₁ ≠ μ₂    

H₀: μ₁ ≠ μ₂
H_a: μ₁ = μ₂

H₀: μ₁ = μ₂
H_a: μ₁ > μ₂

H₀: μ₁ > μ₂
H_a: 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.

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.