Experimental Design and Scientific Method

An acoustic engineer conducts an investigation to measure how changing the thickness of fiberglass insulation panels affects the sound intensity level (in decibels) transmitted through a drywall frame assembly. During all test runs, the sound source frequency is held constant at $1,000\text{ Hz}$, the room temperature is maintained at $22^\circ\text{C}$, and the dimensions of the drywall test frame remain identical. Match each experimental element from the study to its correct variable classification.

Researchers conducted an experiment to evaluate the inhibitory effect of copper sulfate (CuSO4) on the enzymatic activity of catalase, which breaks down hydrogen peroxide (H2O2) into water and oxygen. Four test tubes were prepared under identical temperature and pH conditions:

- Tube 1: 5.0 mL H2O2 solution + 1.0 mL distilled water (No catalase enzyme, no CuSO4)
- Tube 2: 5.0 mL H2O2 solution + 1.0 mL catalase solution (Catalase present, no CuSO4)
- Tube 3: 5.0 mL H2O2 solution + 1.0 mL catalase solution + 0.1 mM CuSO4
- Tube 4: 5.0 mL H2O2 solution + 1.0 mL catalase solution + 1.0 mM CuSO4

Match each experimental setup on the left with its intended baseline or experimental role on the right.

Oceanographers conducted an investigation to determine how variations in seawater salinity affect the vertical settling rates of marine micro-calcite ($CaCO_3$) particles. Synthetic seawater samples were prepared at four salinity levels ($30\ \text{PSU}$, $33\ \text{PSU}$, $35\ \text{PSU}$, and $38\ \text{PSU}$). In each trial, micro-calcite particles of uniform diameter ($50\ \mu\text{m}$) were dropped into a $1\text{-meter}$ vertical settling column maintained at a constant water temperature of $20^\circ\text{C}$. The elapsed transit time required for each particle to sink through the $1\text{-meter}$ distance was recorded to calculate its terminal sinking velocity.

Match each experimental component from the investigation to its correct variable classification.

Geophysicists investigated the seismic wave attenuation properties of synthetic mantle rock (peridotite) under simulated upper mantle conditions.

In Study 1, five cylindrical peridotite samples with average mineral grain sizes ranging from $15\text{ }\mu\text{m}$ to $250\text{ }\mu\text{m}$ were tested at a constant confining pressure of $3.0\text{ GPa}$ and a fixed temperature of $1,200^\circ\text{C}$. A torsional oscillation at a frequency of $1.0\text{ Hz}$ was applied to each sample, and the resulting shear wave attenuation factor ($Q^{-1}$) was recorded.

In Study 2, peridotite samples with a fixed average grain size of $50\text{ }\mu\text{m}$ were held at $1,200^\circ\text{C}$ while the confining pressure was varied from $1.0\text{ GPa}$ to $5.0\text{ GPa}$ to measure $Q^{-1}$.

In Study 3, peridotite samples with a fixed grain size of $50\text{ }\mu\text{m}$ under a constant confining pressure of $3.0\text{ GPa}$ were tested across temperatures from $1,000^\circ\text{C}$ to $1,400^\circ\text{C}$ to measure $Q^{-1}$.

Based on the experimental procedures described, which of the following correctly identifies the independent variable, dependent variable, and one controlled variable for Study 1, respectively?

A botanist conducted a 6-week experiment to evaluate the efficacy of three newly developed organic fertilizers ($F_1$, $F_2$, and $F_3$) on the growth rate of *Solanum lycopersicum* (tomato plants). All groups were maintained under controlled environmental conditions ($22^\circ\text{C}$, 16-hour light cycle). Match each experimental group setup to its corresponding functional role in the experiment.

A student constructs a respirometer apparatus to measure the rate of cellular respiration ($O_2$ consumption) in germinating seeds. Match each component of the apparatus to its primary experimental function in the setup.

Researchers conducted two experiments to investigate the enzymatic activity of cellobiase, an enzyme that hydrolyzes cellobiose into glucose.

*Experiment 1*
Reaction mixtures were prepared using a fixed cellobiase concentration of $0.5\ \text{mg/mL}$ and varying initial cellobiose concentrations ($1.0\ \text{mM}$, $2.5\ \text{mM}$, $5.0\ \text{mM}$, and $10.0\ \text{mM}$). All mixtures were incubated at $37^\circ\text{C}$ and $\text{pH}\ 5.0$. The initial rate of glucose production ($v_0$) was measured for each mixture.

*Experiment 2*
Reaction mixtures were prepared using a constant cellobiose concentration of $5.0\ \text{mM}$ and a constant cellobiase concentration of $0.5\ \text{mg/mL}$. The mixtures were incubated at $\text{pH}\ 5.0$ under four different temperatures ($25^\circ\text{C}$, $37^\circ\text{C}$, $50^\circ\text{C}$, and $65^\circ\text{C}$). The initial rate of glucose production ($v_0$) was measured for each mixture.

Based on the descriptions of both experiments, which variable served as the independent variable in Experiment 1 but was maintained as a controlled variable in Experiment 2?

A team of microbiologists investigated the impact of synthetic micro-plastic additives ($P_1$ and $P_2$) on the rate of nitrogen fixation by *Rhizobium* bacteria in soil culture vessels. Four identical culture vessels were prepared and incubated at $22^\circ\text{C}$ with $15\%$ baseline soil moisture for 14 days under the following conditions:

- Vessel 1: Standard nutrient medium + live *Rhizobium* bacteria (no plastic additives)
- Vessel 2: Standard nutrient medium + sterile (non-viable) *Rhizobium* bacteria + additive $P_1$
- Vessel 3: Standard nutrient medium + live *Rhizobium* bacteria + additive $P_1$
- Vessel 4: Standard nutrient medium + live *Rhizobium* bacteria + additive $P_2$

Match each experimental vessel on the left with its intended role in establishing control conditions or testing experimental variables on the right.

Scientists conducted an experiment to evaluate how hydroxyl radicals ($\text{OH}$) and ultraviolet ($\text{UV}$) light interact to break down atmospheric methane ($\text{CH}_4$). Four identical gas-tight reaction vessels were maintained at $25^\circ\text{C}$ with an initial concentration of $2.0\text{ ppm}$ $\text{CH}_4$. Each vessel was subjected to different conditions of $\text{OH}$ radical presence and $\text{UV}$ light intensity for a duration of 12 hours:

After 12 hours, the remaining concentration of $\text{CH}_4$ was recorded for each vessel.

To determine the specific effect of increasing $\text{UV}$ light intensity on the degradation rate of $\text{CH}_4$ in the presence of $\text{OH}$ radicals, which vessel serves as the control group?

A team of atmospheric chemists investigated the photochemical formation of secondary organic aerosols (SOAs) in a $5\text{ m}^3$ Teflon smog chamber. Across four distinct experimental runs, researchers introduced constant initial concentrations of $\alpha$-pinene ($100\text{ ppb}$) and ozone ($200\text{ ppb}$) into the chamber alongside ammonium sulfate seed aerosols ($15\ \mu\text{g/m}^3$). Chamber temperature was maintained at $298\text{ K}$ and relative humidity at $50\%$. The ultraviolet (UV) light irradiance was set to a different value for each run ($0\text{ W/m}^2$, $25\text{ W/m}^2$, $50\text{ W/m}^2$, or $100\text{ W/m}^2$). After 4 hours of continuous irradiation, the researchers measured the final total SOA mass concentration ($\mu\text{g/m}^3$) produced in the chamber.

Match each experimental component to its correct variable classification.

A student performed an experiment to study the catalytic decomposition of hydrogen peroxide ($H_2O_2$). In 5 separate trials, the student added $5\text{ mL}$ of a ferric nitrate ($Fe(NO_3)_3$) solution of varying concentrations ($0.1\text{ M}$, $0.2\text{ M}$, $0.3\text{ M}$, $0.4\text{ M}$, and $0.5\text{ M}$) to $50\text{ mL}$ of $3\%\text{ }H_2O_2$ solution in a sealed reaction flask connected to a gas syringe. The initial temperature of all solutions was maintained at $22^\circ\text{C}$. For each trial, the volume of oxygen gas ($O_2$) produced in the first $30\text{ seconds}$ was recorded to determine the initial reaction rate.

Based on the experimental procedure described, which of the following was the independent variable in the student's experiment?

Aerospace engineers conducted a series of wind tunnel trials to evaluate passive boundary layer control on a swept-wing model using micro-vortex generators (VGs). In Experiment 1, the engineers intentionally varied the VG orientation angle relative to the freestream flow ($\theta$) across five trials while maintaining a constant freestream velocity ($v = 45\text{ m/s}$), wing angle of attack ($\alpha = 12^\circ$), and ambient temperature ($T = 20^\circ\text{C}$). For each trial, they recorded the normalized chordwise position of boundary layer separation ($x_s/c$). Their data are shown in the table below:

Based on Experiment 1, which of the following correctly identifies the independent variable, the dependent variable, and one controlled variable?

An environmental science team investigated the effects of soil moisture on soil microbial respiration rates. In five experimental plots, they adjusted the soil volumetric water content to values ranging from $10\%$ to $50\%$. Throughout all trials, they kept the soil temperature constant at $22^\circ\text{C}$ and maintained a uniform soil bulk density. At the end of 48 hours, they measured the total carbon dioxide ($CO_2$) efflux from each plot.

Match each experimental component listed on the left with its correct variable classification on the right.

A team of plant physiologists investigated the effect of a chemical surfactant (Surfactant X) on the water retention capacity of corn seedlings (*Zea mays*) during a simulated drought.

Four experimental groups of 20 corn seedlings each were grown in identical pots containing 500 g of soil:
- Group 1 was watered with 100 mL of pure distilled water.
- Group 2 was watered with 100 mL of a 0.1% Surfactant X aqueous solution.
- Group 3 was watered with 100 mL of a 0.5% Surfactant X aqueous solution.
- Group 4 was watered with 100 mL of a 1.0% Surfactant X aqueous solution.

All groups were maintained in the same environmental chamber at $25^\circ\text{C}$ with 14 hours of light daily. After 14 days, the average change in seedling biomass was recorded.

Which group served as the control group in this experiment, and what baseline condition did it establish?

A team of biomechanical engineers investigated how stride frequency influences peak knee joint contact force during treadmill running. Ten distance runners completed four trials on an instrumented treadmill at a constant running velocity of $4.0\text{ m/s}$ while wearing identical running shoes. Across trials, stride frequency was set to $150$, $160$, $170$, or $180\text{ steps/min}$ using a rhythmic auditory metronome. Sensors in the treadmill measured the peak knee joint contact force in body weights ($\text{BW}$) during each stance phase. Which of the following identifies the dependent variable in this experiment?

Biomechanical engineers investigated how the initial knee flexion angle affects the peak vertical ground reaction force generated by athletes during a countermovement jump on a stationary force plate. In the experiment, athletes performed jumps starting from pre-determined knee flexion angles (30°, 45°, 60°, and 75°), while force plate sensors continuously recorded the maximum force exerted against the platform during takeoff. All trials were conducted using the same athlete cohort wearing identical athletic footwear under standardized indoor temperature and humidity conditions. Based on this experimental design, match each experimental component to its corresponding variable classification.

Experiment 1

A student constructs an electrolytic cell apparatus to measure the rate of copper electroplating. As shown in the setup, a nickel cathode strip is submerged in an aqueous $1.0\text{ M } \text{CuSO}_4$ solution alongside a copper anode. Both electrodes are connected to a DC power supply and an ammeter. Before turning on the power supply, the student thoroughly washes the nickel cathode with distilled water and acetone, allows it to dry completely, and measures its mass on an analytical balance.

What is the primary procedural purpose of drying the nickel cathode completely before recording its initial mass?

A team of biogeochemists investigated anaerobic oxidation of methane by marine sediment microbes under simulated deep-sea temperature conditions ($4^\circ\text{C}$). Four distinct reactor setups were prepared containing equal masses of marine sediment and methane gas, but with varying additions of electron acceptors, heat sterilization, and hydrostatic pressures.

Match each experimental setup to its corresponding role or baseline function in the experiment.

A marine biologist conducted an experiment to evaluate how water flow velocity affects the peak bioluminescence intensity produced by the dinoflagellate *Pyrocystis fusiformis*. In four separate experimental trials, cell cultures were exposed to flow velocities of $0.1\text{ m/s}$, $0.5\text{ m/s}$, $1.0\text{ m/s}$, and $2.0\text{ m/s}$. In each trial, the cell density ($1{}000\text{ cells/mL}$), water temperature ($20^\circ\text{C}$), and ambient light intensity ($0\text{ lux}$) were kept constant.

Match each experimental variable category on the left with its corresponding component from the experiment on the right.

A marine geochemist conducted an experiment to evaluate the effect of ocean depth on the dissolution rate of calcium carbonate ($\text{CaCO}_3$). Four sealed pressure vessels were filled with seawater kept at a constant temperature of $2^\circ\text{C}$ and a fixed salinity of $35\text{ psu}$. The hydrostatic pressure in each vessel was set to a different specific level: $100\text{ atm}$, $200\text{ atm}$, $300\text{ atm}$, or $400\text{ atm}$. A synthetic calcite pellet with an initial mass of $5.00\text{ g}$ was placed in each vessel. After $48\text{ hours}$, the pellet was removed and weighed to determine the total mass of dissolved $\text{CaCO}_3$ (in milligrams). Which of the following correctly identifies the independent variable and one of the controlled variables in this experiment?