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 |
---|---|

n |
n |

y |
y |

s |
s |

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

State the null and alternative hypotheses.

*H*_{0}: μ_{1} = μ_{2}

*H*_{a}: μ_{1} <
μ_{2}

*H*_{0}: μ_{1} = μ_{2}

*H*_{a}: μ_{1} ≠
μ_{2}

*H*_{0}: μ_{1} ≠ μ_{2}

*H*_{a}: μ_{1} = μ_{2}

*H*_{0}: μ_{1} = μ_{2}

*H*_{a}: μ_{1} >
μ_{2}

*H*_{0}: μ_{1} > μ_{2}

*H*_{a}: μ_{1} = μ_{2}

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

y_{1} − y_{2}.)

z =

What is the conclusion of your test?

Fail to reject H_{0}. There is not enough evidence to
conclude the mean shear strength for the two soil types is
different.

Reject H_{0}. There is not enough evidence to conclude
the mean shear strength for the two soil types is
different.

Fail to reject H_{0}. There is enough evidence to
conclude the mean shear strength for the two soil types is
different.

Reject H_{0}. 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 H _{0}. There is enough
evidence to conclude the mean shear strength for the two soil types
is different.**

Shear strength measurements derived from unconfined compression
tests for two types of soils gave the results shown in the
following summary statistics (measurements in tons per square
foot).
Summary Statistics
Soil Type I: Sample size = 25, Sample mean = 1.65, Sample std =
0.26
Soil Type II: Sample size = 31, Sample mean = 1.43, Sample std =
0.22.
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