A student proposed the following hypothesis regarding soil drainage: *Hypothesis*: Soil pe… — ACT

A student proposed the following hypothesis regarding soil drainage:

*Hypothesis*: Soil permeability (the rate at which water flows through soil) is determined by the average particle size of the soil, such that soils with larger average particle sizes will always have higher water flow rates, regardless of the compaction level of the soil.

To test this hypothesis, the student measured the water flow rate, in milliliters per minute ( $\text{mL/min}$ ), through three different soil samples under both uncompacted and compacted conditions. The results are shown in the table below.

Soil Sample	Average Particle Size ( $\text{mm}$ )	Flow Rate - Uncompacted ( $\text{mL/min}$ )	Flow Rate - Compacted ( $\text{mL/min}$ )
X	$0.1$	$15$	$3$
Y	$0.5$	$45$	$12$
Z	$2.0$	$120$	$8$

Based on these results, do the data support the student's hypothesis?

A
Yes; under both uncompacted and compacted conditions, the flow rate increased as the average particle size increased from Soil X to Soil Z.
B
Yes; the flow rate of each soil sample was higher under uncompacted conditions than under compacted conditions.
No; under compacted conditions, Soil Z had a lower flow rate than Soil Y, even though Soil Z has a larger average particle size.Answer
D
No; under uncompacted conditions, Soil Y had a higher flow rate than Soil X, which contradicts the hypothesis.

Answer

No; under compacted conditions, Soil Z had a lower flow rate than Soil Y, even though Soil Z has a larger average particle size.

The correct answer is the option stating that under compacted conditions, Soil Z had a lower flow rate than Soil Y, even though Soil Z has a larger average particle size. The student's hypothesis states that soils with larger average particle sizes will always have higher flow rates, regardless of compaction level. However, the data show that in compacted conditions, Soil Z (average particle size

2.0\text{ mm}

) has a water flow rate of

8\text{ mL/min}

, which is lower than that of Soil Y (average particle size

0.5\text{ mm}

, flow rate

12\text{ mL/min}

). This direct contradiction means the hypothesis is not supported by the data.

Step-by-Step Solution

Identify the student's hypothesis and the conditions it applies to.

The hypothesis asserts that soils with larger average particle sizes will always have higher flow rates, regardless of the compaction level.

This establishes the rule that the experimental data must satisfy in order to support the hypothesis.

Examine the data for both uncompacted and compacted conditions.

In uncompacted conditions, flow rates increase as particle size increases (

15 < 45 < 120\text{ mL/min}

). In compacted conditions, the flow rate increases from Soil X (

3\text{ mL/min}

) to Soil Y (

12\text{ mL/min}

), but decreases for Soil Z (

8\text{ mL/min}

), which has the largest particle size.

Evaluating each set of conditions separately is required because the hypothesis states the relationship must hold true regardless of compaction level.

Compare the behavior under compacted conditions to the hypothesis.

Under compacted conditions, Soil Z (particle size

2.0\text{ mm}

) has a lower flow rate than Soil Y (particle size

0.5\text{ mm}

), showing that a larger particle size does not always lead to a higher flow rate.

A single contradiction is sufficient to refute the student's hypothesis.

Key Concept

Formulating and Modifying Hypotheses based on experimental results and identifying counterexamples.

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