Scientific question hypothesis and evidence

A scientific question addresses nature and admits an answer obtained by measurement: "Is the sky beautiful?" is not one, while "How does the period of a pendulum depend on its length?" is. A hypothesis is a proposed, testable answer to such a question, phrased so that it can turn out to be wrong: if the length is $L$ and the period is $T$, then doubling $L$ should increase $T$ by the factor $\sqrt{2}$. A hypothesis becomes useful only when it yields a prediction — a statement of the form if …, then … that can be checked against data.

Evidence is the set of observations or measurements that could refute the prediction; a claim resting only on opinion or authority is not evidence, because nothing could count against it. A sound test isolates one independent variable, measures one dependent variable, and holds the controlled variables constant, so that a change in the outcome can be attributed to the cause you actually changed. The result of a test is never final proof: it either fails to refute the hypothesis, raising confidence in it, or it refutes the hypothesis and forces a revision.

Given the claim "Music makes students better at mathematics". Turn it into (a) a scientific question that measurement can answer, (b) a falsifiable if–then hypothesis, and (c) name the independent and dependent variables.

A student investigates whether warm water dissolves sugar faster. She puts the same mass of sugar $m = 5\ \text{g}$ into $200\ \text{mL}$ of water at $20\ ^\circ\text{C}$, $40\ ^\circ\text{C}$ and $60\ ^\circ\text{C}$, stirs each glass five times, and stops the timer when no crystals are visible.

(a) State a falsifiable hypothesis. (b) Identify the independent, dependent and controlled variables. (c) Does this data set support the hypothesis, refute it, or leave the question open?

A gardener claims that a new fertilizer raises the tomato yield. He applies the fertilizer to the field by the river, which also receives more water and more sun, and leaves his far field untreated. He reports $3.1\ \text{kg}$ per plant versus $2.2\ \text{kg}$ per plant and concludes that the fertilizer works.

(a) Name the flaw in the design using the vocabulary of variables. (b) Rewrite the test so that only one independent variable changes. (c) State exactly what observation would refute the fertilizer hypothesis.

Goal: run the full cycle "question → hypothesis → prediction → evidence" on a safe pendulum example.

Plan (self-study, 30–40 minutes):

1. Choose the question: "How does the period $T$ of a pendulum depend on the suspension length $L$?"
2. Write the hypothesis and the prediction: if $L$ is doubled, then $T$ increases by the factor $\sqrt{2}$.
3. Run the test safely: use a computer simulation (for example, Pendulum Lab) or, if you prefer real measurements, hang a mass of no more than $100\ \text{g}$ on a string no longer than $1\ \text{m}$, away from people, glass and walkways, and keep the mass from striking objects. Never work with mercury, open flame, high voltage or sharp edges; study anything involving such hazards only in a simulation.
4. Fix the variables: independent — $L \in \{0.25;\ 0.50;\ 1.00\}\ \text{m}$, dependent — $T$ (the mean of three measurements), controlled — the mass of the bob, the amplitude (no more than $10^\circ$), and the way you start the motion.
5. Record the data in a table and plot $T$ against $L$.
6. Draw one of three conclusions: the data do not refute the hypothesis, they refute it, or they are insufficient. State explicitly which measurement would make you change the hypothesis.

Show how a testable question turns into a hypothesis and a prediction, and how evidence either refutes or fails to refute it; make the three variable roles visible at a glance.

A flow diagram of five labelled boxes joined by arrows: Question → Hypothesis → Prediction (if …, then …) → Test and evidence → Conclusion, with a feedback arrow from "Conclusion" back to "Hypothesis" labelled "revise". Below it, a three-row table matching the independent, dependent and controlled variables to the example from Worked Example 2.

A 15-year-old asks: does a higher release angle improve free-throw success? She sets distance to the hoop $4.6\ \mathrm{m}$, release height $2.1\ \mathrm{m}$, and ball speed $7.0\ \mathrm{m/s}$. Hypothesis: increasing release angle from $45^\circ$ to $55^\circ$ raises the fraction of successful shots because the ball enters the hoop at a steeper angle. Evidence: 50 throws at each angle, with the same ball mass $0.62\ \mathrm{kg}$ and same release height: $18/50$ successes at $45^\circ$, $29/50$ at $55^\circ$.

This exercises the link question → measurable hypothesis → evidence: the question is narrowed to one independent variable (angle), one dependent count (successes), and controlled quantities (distance, height, speed, mass).

A pupil asks: does switching a phone to airplane mode shorten charging from 20% to 80%? Hypothesis: with the screen off and the same $20\ \mathrm{W}$ charger, airplane mode reduces charging time by at least $5\ \mathrm{min}$ because the radio transmitter is off. Evidence from one phone: from 20% to 80% it takes $72\ \mathrm{min}$ with normal radios and $65\ \mathrm{min}$ in airplane mode; battery capacity is $4500\ \mathrm{mAh}$ at $3.8\ \mathrm{V}$.

It shows how evidence is collected as a controlled comparison with one changed condition, so the measured time difference can support or contradict the hypothesis rather than personal impression.

While cooking pasta, a student asks: does adding $20\ \mathrm{g}$ of salt to $1.0\ \mathrm{L}$ of water make it boil sooner? Hypothesis: it will boil about $20\ \mathrm{s}$ sooner because salt helps bubbles form. Evidence: starting at $20^\circ\mathrm{C}$ and using a $2.0\ \mathrm{kW}$ stove setting, pure water reaches $100^\circ\mathrm{C}$ in $4\ \mathrm{min}\ 10\ \mathrm{s}$; salted water reaches about $100.2^\circ\mathrm{C}$ in $4\ \mathrm{min}\ 25\ \mathrm{s}$.

This uses the requirement that a hypothesis yield a numerical prediction: the prediction is $-20\ \mathrm{s}$, but the measurement is $+15\ \mathrm{s}$, so the evidence contradicts the hypothesis and raises a new question about boiling-point elevation.