Paper Towel Absorbency Claim
The student council wants to choose the most absorbent paper towel. Students test three brands. They cut Brand X and Brand Y into 10 cm by 10 cm squares, but cut Brand Z into a 15 cm by 15 cm square. Each sample receives 20 mL of water, sits for 30 seconds, and is squeezed into a graduated cylinder. One trial per brand gives X 8 mL, Y 12 mL, and Z 15 mL. The student council announces that Z is best because it released the most water. A student objects that Z was larger. The teacher asks the class to evaluate the claim, identify what should be held constant, and use the data to compare absorbency fairly. The students have a balance available and can repeat trials.
1. Identify the main flaw in the student council's conclusion and explain which variables should be controlled in a fair test.
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The main flaw is that the samples were not the same size. Brand Z had an area of 225 cm2, while X and Y each had 100 cm2. A larger piece has more paper fibers and can hold more water, so Z's 15 mL may reflect its size rather than greater absorbency per unit of paper. Other variables also need control: the amount of water, soak time, squeezing force and duration, water temperature, and number of trials. One trial per brand is also weak because natural variation could affect the result. A fair test should use equal areas or equal masses of each brand, apply the same water volume and soak time, squeeze each sample the same way, and repeat several trials to calculate a mean. Only then can the released water be compared meaningfully.
2. The sample masses are X 1.0 g, Y 1.2 g, and Z 2.4 g. Calculate milliliters of water released per gram and per square centimeter, and interpret the results.
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Per gram: X is 8 mL / 1.0 g = 8.0 mL/g; Y is 12 mL / 1.2 g = 10.0 mL/g; Z is 15 mL / 2.4 g = 6.25 mL/g. Per square centimeter: X is 8 mL / 100 cm2 = 0.08 mL/cm2; Y is 12 mL / 100 cm2 = 0.12 mL/cm2; Z is 15 mL / 225 cm2 = about 0.067 mL/cm2. On both normalized measures, Y is the most absorbent, while Z is actually the least absorbent per gram and per area. The raw volume of 15 mL made Z look best only because the sample was much larger and heavier. The council should compare normalized values, not total water released from unequal samples.
3. Write a response to the student council and describe a revised procedure that would produce defensible evidence.
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The response should say that Z's 15 mL cannot be compared directly with X's 8 mL and Y's 12 mL because Z had more than twice the area and mass. When the data are adjusted, Y releases the most water per gram and per square centimeter. A revised procedure should cut all brands to the same size, such as 10 cm by 10 cm, or use equal masses if thickness varies. Give each sample the same 20 mL of water and the same 30-second soak. Use the same squeezing method and time, and have the same person squeeze each sample or use a consistent press. Run at least three trials per brand, calculate the mean, and report milliliters per gram or per square centimeter. The council should base its choice on those normalized, repeated results rather than on a single raw volume.