Scientific Reasoning & Conflicting Viewpoints

Hypotheses, conclusions, applying results and comparing scientists’ viewpoints.

Worked Examples

<details> <summary><b>Example 1: Name every variable in a study</b></summary>

Study: A student released identical toy cars from heights of 10 cm, 20 cm, 30 cm, and 40 cm on the same ramp. Each car rolled off the ramp onto the same strip of carpet. She ran three trials at each height and recorded the average distance each car rolled across the carpet.

Question: Identify the independent variable, the dependent variable, and two controlled variables.

Solution:

1. What did she change on purpose? The release height. That is the independent variable.
2. What did she measure? The distance rolled across the carpet. That is the dependent variable.
3. What stayed the same? The type of car and the carpet surface (also the ramp). Those are controlled variables. Because every car rolled on the same carpet, the carpet cannot explain why some cars went farther.
4. What is NOT a controlled variable? Anything the passage never mentions, such as the humidity in the room. You cannot assume it was held constant.

Answer: Independent = release height; dependent = distance rolled; controlled = car type and carpet surface. ✓

</details> <details> <summary><b>Example 2: Classify the statements in a lab report</b></summary>

Report excerpt:

1. "Our bean plants on the windowsill leaned toward the glass."
2. "If a plant receives light from only one side, its stem will bend toward that side."
3. "Five of the six plants lit from the left bent left by 10° to 25°."
4. "Light from one direction caused the stems to bend toward it."

Question: Which statement is the hypothesis, and which is the conclusion?

Solution:

1. Statement 1 is something noticed before any test: an observation.
2. Statement 2 is an "if... then" prediction that a test could prove wrong: the hypothesis.
3. Statement 3 reports measured results: data.
4. Statement 4 interprets the data: the conclusion.

Answer: Hypothesis = statement 2; conclusion = statement 4. ✓

Skill: Data are numbers and measurements; a conclusion says what those numbers mean.

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Worked Examples

<details> <summary><b>Example 1: A "Yes, because / No, because" question</b></summary>

Study: A student hypothesized, "The activity of Enzyme K increases as temperature increases." She measured activity (in units) at five temperatures.

Question: Do the results support her hypothesis?

• A. Yes, because activity rose from 20°C to 40°C.
• B. Yes, because the highest activity occurred at a middle temperature.
• C. No, because activity fell at temperatures above 40°C.
• D. No, because only five temperatures were tested.

Solution:

1. Prediction: activity should rise across the whole range.
2. Data: it rises to 40°C, then falls to 6 units at 60°C. The prediction fails above 40°C, so the answer is No.
3. Pick the reason: C names the data that contradict the claim. D is a weak reason; five temperatures are plenty to reveal the pattern. A and B start with "Yes," which is already wrong.

Answer: C ✓

</details> <details> <summary><b>Example 2: Which result would weaken an "only" hypothesis?</b></summary>

Hypothesis: "The time a cup of water takes to cool from 80°C to 40°C depends only on the volume of water."

Question: Which result would contradict this hypothesis?

• A. 200 mL cooled more slowly than 100 mL in identical cups.
• B. Two 150 mL samples in identical cups cooled in the same time.
• C. 300 mL cooled more slowly than 200 mL in identical cups.
• D. Two 150 mL samples, one in a foam cup and one in a metal cup, cooled in very different times.

Solution:

1. If volume is the only factor, equal volumes must cool in equal times.
2. D holds volume fixed and still gets different times, so the cup material matters too. That breaks "only."
3. A and C show volume mattering, which the hypothesis allows. B is exactly what the hypothesis predicts.

Answer: D ✓

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Worked Examples

<details> <summary><b>Example 1: A trend with a peak</b></summary>

Study: Students counted the oxygen bubbles released per minute by a sprig of pondweed in water at different temperatures.

Question: Which statement best describes the relationship, and what can be said about the best temperature?

Solution:

1. Trace every point: 6 → 14 → 22 rises; 22 → 15 → 5 falls. The pattern is increases, then decreases.
2. Endpoints trap: 6 and 5 are nearly equal, so looking only at the ends would wrongly suggest "no change."
3. Scope: Of the temperatures tested, bubbling was fastest at 30°C. The true peak could be anywhere between 20°C and 40°C, so "exactly 30°C" goes too far.

Answer: Bubbling increased up to 30°C, then decreased; 30°C was the best tested temperature. ✓

</details> <details> <summary><b>Example 2: Association versus cause</b></summary>

Study: A survey of 300 households found that homes with more houseplants reported fewer colds per person each winter.

Question: Which conclusion is best supported?

• A. Houseplants prevent colds by cleaning indoor air.
• B. Catching fewer colds makes people buy more houseplants.
• C. The number of houseplants is associated with the number of colds.
• D. Houseplants and colds are unrelated, because no cause was found.

Solution:

1. Kind of study: a survey, so it can show an association but not a cause.
2. A claims a cause and adds a mechanism (air cleaning) the survey never measured. B claims the reverse cause, also untested.
3. D contradicts the data: the two counts clearly vary together.
4. A third factor, such as time spent at home or household income, could explain both.

Answer: C ✓

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Worked Examples

<details> <summary><b>Example 1: Extending an inverse pattern</b></summary>

Study: Engineers timed how long identical pumps, working together, took to fill the same tank.

Question: If the pattern continues, how long would 5 pumps take?

Solution:

1. Test for linear: the drops are 30, 10, 5 minutes for equal steps, so the time does not fall by a fixed amount.
2. Test for inverse: 1 × 60 = 60, 2 × 30 = 60, 3 × 20 = 60, 4 × 15 = 60. The product is constant.
3. Extend: time = 60 ÷ 5 = 12 min.
4. Trap: continuing the last drop (5 minutes) would give 10 min, which breaks the constant product.

Answer: 12 min ✓

</details> <details> <summary><b>Example 2: Combining two experiments</b></summary>

Experiment 1 (all radish plants at 20°C): 0 g of fertilizer → 3.0 cm of growth per week; 2 g → 4.5 cm; 4 g → 6.0 cm.

Experiment 2 (all plants given 2 g of fertilizer): 10°C → 2.0 cm per week; 20°C → 4.5 cm; 30°C → 3.5 cm.

Question: Predict weekly growth with 4 g of fertilizer at 10°C.

Solution:

1. Start from a shared condition: 4 g of fertilizer gave 6.0 cm, measured at 20°C.
2. Adjust with the other experiment: at 2 g, dropping from 20°C to 10°C cut growth from 4.5 cm to 2.0 cm. Cooler means slower.
3. Combine: 4 g at 10°C should be less than 6.0 cm. Choosing "more than 6.0 cm" ignores temperature; choosing "exactly 2.0 cm" ignores the extra fertilizer.

Answer: less than 6.0 cm ✓

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Worked Examples

<details> <summary><b>Example 1: Comparing two series</b></summary>

Data: Rate of gas production (mL per minute) when a catalyst is added to a peroxide solution.

Question: Which statement is supported by the data?

• A. At both temperatures, the rate rose with catalyst mass and was higher at 25°C.
• B. At both temperatures, the rate fell with catalyst mass and was higher at 35°C.
• C. At both temperatures, the rate rose with catalyst mass and was greater at 35°C.
• D. The rate rose with catalyst mass at 25°C but fell at 35°C.

Solution:

1. Trend in each column: both columns increase going down, so the rate rose with catalyst mass at both temperatures. That eliminates B and D.
2. Which column is higher? In every row, the 35°C value is larger (3.0 > 2.1, 5.8 > 4.0, 11.2 > 7.9). That eliminates A.

Answer: C ✓

Skill: Split a two-part statement into its parts and test each part separately.

</details> <details> <summary><b>Example 2: Absolute versus relative change</b></summary>

Data: Grams of three compounds that dissolve in 100 mL of water.

Question: Which compound's solubility increased by the greatest number of grams?

Solution:

1. Compute each change in grams: J: 58 − 50 = 8 g; K: 26 − 6 = 20 g; L: 115 − 90 = 25 g.
2. Largest absolute change: Compound L (25 g).
3. Trap: Compound K more than quadrupled, the largest relative change, but the question asks about grams.

Answer: Compound L ✓

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Worked Examples

<details> <summary><b>Example 1: Agreement and decisive evidence (two students)</b></summary>

Passage: The population of a songbird on a small island fell by half over 10 years.

Student 1: Rats that arrived on supply boats eat the eggs and chicks. The rats are the main cause of the decline.

Student 2: Rainfall on the island has dropped during the 10 years. With less rain, there are fewer insects, so many chicks starve before leaving the nest.

Question 1: Both students would most likely agree that:

• A. rats eat songbird eggs.
• B. fewer chicks have survived to adulthood.
• C. rainfall on the island has decreased.
• D. insects are the birds' main food.

Question 2: Which finding would support Student 1 but NOT Student 2?

• A. The bird population has fallen.
• B. Chicks in the remaining nests weigh less than chicks did 10 years ago.
• C. On a nearby island with no rats but the same drop in rainfall, the songbird population stayed steady.
• D. Rainfall dropped by 30% during the decade.

Solution:

1. Q1: Both explanations end with fewer chicks surviving; they differ on why. A belongs only to Student 1; C and D belong only to Student 2. Answer: B
2. Q2: Choice C shows the same drought with no rats and no decline, which fits Student 1 and contradicts Student 2. A fits both. B and D support Student 2. Answer: C ✓

</details> <details> <summary><b>Example 2: Three viewpoints and one result</b></summary>

Passage: A burning candle is covered with a glass jar and goes out after a few seconds.

Student 1: The flame uses up the oxygen in the jar, and it goes out when no oxygen is left. Student 2: The flame produces carbon dioxide, which builds up until it smothers the flame. Student 3: Heat trapped in the jar makes the wax melt so fast that it floods the wick.

Question: A candle in a jar kept cold in an ice bath went out after the same time as a candle in a room-temperature jar. This result is consistent with which students?

Solution:

1. Student 3 says trapped heat puts the flame out, so keeping the jar cold should make the candle last longer. It did not, so the result weakens Student 3.
2. Students 1 and 2 blame changes in the gases, which an ice bath would not prevent. The result fits both.

Answer: Students 1 and 2 only ✓

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Worked Examples

<details> <summary><b>Example 1: Choosing the best experimental design</b></summary>

Question: A student wants to test whether the color of a pot affects how warm the soil inside it gets in sunlight. Which design is best?

• A. Pots of different colors and different sizes, each filled with soil and placed in the sun.
• B. Identical pots in different colors, filled with the same soil, placed side by side in the sun.
• C. Identical black pots filled with the same soil, some in sun and some in shade.
• D. Pots of different colors, with the black pot indoors and the others outdoors.

Solution:

1. Variable to test: pot color. It must change, and nothing else should.
2. A changes size along with color; D changes location along with color. Either extra factor could explain the result.
3. C never changes color, so it cannot answer the question.
4. B changes only color and holds pot type, soil, and location constant.

Answer: B ✓

</details> <details> <summary><b>Example 2: Testing a cause after a correlation</b></summary>

Situation: A researcher finds that students who eat breakfast earn higher morning quiz scores.

Question: Which follow-up study would best test whether eating breakfast causes higher scores?

Solution:

1. The original finding is a correlation: students who eat breakfast may differ in sleep, schedules, or other habits.
2. Surveying more students, or asking them whether breakfast helps, still measures only an association or an opinion.
3. Randomly assigning students to eat or skip breakfast on test days makes the groups alike except for breakfast, so a difference in scores can be traced to it.

Answer: Randomly assign breakfast, then compare scores. ✓

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