Read each question scenario and the statements below it. Click on the ONE statement/step you believe is INCORRECT. The explanation for why the indicated answer is incorrect will appear after you click any option.
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Identify the independent variable in this investigation (comparing biodiversity under different tree plantations in Bangladesh).
Click the INCORRECT identification of the independent variable:
- The location within Bangladesh.
- The species of tree used in the plantation.
- The biodiversity index calculated.
- The type of tree (alien vs indigenous).
Reason Incorrect (C): The independent variable is the factor intentionally changed or categorized by the researchers to observe its effect. In this study, the researchers are comparing plantations based on the type or species of tree (Options B and D correctly relate to this). The biodiversity index (#C) is what is measured as an outcome to see if it *depends* on the tree type, making it the dependent variable, not the independent variable. Location (#A) would ideally be a controlled variable.
Identify two variables the scientists standardised (kept constant) in the plantation biodiversity study.
Click the variable that was measured (dependent) or changed (independent), NOT standardised:
- Size/area of the sampling plot (36m x 36m).
- Number of undergrowth species found.
- Timing of sampling (same months/seasons – April, July, November).
- Method used for sampling (belt transect).
- Number of plantations sampled per tree species (three).
Reason Incorrect (B): Standardised variables are factors kept the same across all experimental groups to ensure a fair comparison. Plot size (A), timing (C), sampling method (D), and number of sites per tree type (E) were likely controlled. The number of undergrowth species found (B) is a component of the biodiversity measurement – it’s a result or outcome (part of the dependent variable), not something standardised beforehand.
Describe how belt transects could be used to collect data on the abundance of different plant species in the undergrowth… within one of the 36m x 36m plots.
Click the step that is IRRELEVANT to this specific procedure:
- Place a quadrat (e.g., 1m x 1m) at regular intervals (or contiguously) along the transect, identifying and recording the abundance (e.g., count individuals or % cover) of each undergrowth plant species within it each time.
- Use multiple belt transects (at least 3) within each plot, placed randomly or systematically, to ensure the sample is representative of the whole plot.
- Estimate the height of the tallest tree in the plot.
- Lay down two parallel measuring tapes (e.g., 30m long, 1m apart) across a representative area to mark the boundaries of the belt transect.
- Use a plant identification key or field guide to accurately identify the different undergrowth species encountered within the quadrats.
- Be aware of potential safety hazards like uneven terrain or thorny plants while conducting fieldwork.
Reason Incorrect (C): The objective is to assess the abundance of undergrowth plant species using belt transects and quadrats to calculate a diversity index. Measuring the height of the canopy trees (#C) provides information about the plantation structure but is not part of the procedure for sampling the undergrowth vegetation abundance itself. Steps A, B, D, and E describe relevant parts of the sampling method, and F is a safety consideration.
Mean Simpson’s Index (D) values…: Acacia (alien) = 0.88±0.02; Eucalyptus (alien) = 0.85±0.02; Sal tree (native) = 0.94±0.00; Mango (native) = 0.88±0.02. State and explain whether this data supports the hypothesis: ‘The undergrowth in plantations of alien tree species will have a lower biodiversity… than… indigenous tree species.’
Click the INCORRECT conclusion or observation:
- Conclusion: The data fully supports the hypothesis because both alien species have lower mean D values than both native species.
- Observation contradicting hypothesis: The mango plantation (native) has the same mean D value (0.88) as the acacia plantation (alien), challenging the idea that *all* native are higher than *all* alien.
- Observation supporting hypothesis: The sal tree plantation (native) shows the highest mean D value (0.94), which is higher than both alien species (Acacia 0.88, Eucalyptus 0.85).
- Observation supporting hypothesis: The eucalyptus plantation (alien) shows the lowest mean D value (0.85), which is lower than both native species (Sal 0.94, Mango 0.88).
- Consideration: Standard deviations are small but suggest potential overlap (e.g., 0.88±0.02 for Acacia and Mango), meaning some differences might not be statistically significant without further testing.
- Overall Conclusion: The data provides mixed or partial support for the hypothesis, rather than full, unequivocal support.
Reason Incorrect (A): Statement (A) claims the data *fully* supports the hypothesis. This is incorrect because one of the native species (Mango, D=0.88) has the *same* mean biodiversity index as one of the alien species (Acacia, D=0.88), as pointed out in statement (B). While Sal tree (native) is higher than both aliens, and Eucalyptus (alien) is lower than both natives (statements C & D), the equivalence of Mango and Acacia means the hypothesis isn’t fully supported across all comparisons. Therefore, the overall conclusion should be mixed or partial support (F).
Describe how to prepare 50 cm³ of 2.5 mg cm⁻³ solution from a 10 mg cm⁻³ stock solution of root extract using distilled water.
Click the INCORRECT step or value:
- Calculate stock volume needed using the dilution formula C1V1 = C2V2 or ratio: Volume_Stock = (Desired_Conc / Stock_Conc) * Final_Vol = (2.5 / 10) * 50 cm³ = 12.5 cm³.
- Measure 37.5 cm³ of distilled water accurately using a measuring cylinder or pipette.
- Measure 12.5 cm³ of the stock solution accurately and add it to the measured distilled water, then mix thoroughly (or add stock to flask and make up to 50 cm³).
- Calculate water volume needed: Final Volume – Stock Volume = 50 cm³ – 12.5 cm³ = 37.5 cm³.
- Measure 2.5 cm³ of stock solution using a pipette.
Reason Incorrect (E): The calculation in step (A) correctly determines that 12.5 cm³ of the stock solution is required to make 50 cm³ of the desired 2.5 mg cm⁻³ solution (a 1 in 4 dilution). Measuring only 2.5 cm³ of the stock solution (#E) would result in a final concentration of (10 mg/cm³ * 2.5 cm³) / 50 cm³ = 0.5 mg cm⁻³, which is incorrect. Steps A, B, C, and D describe correct calculations or procedures.
Describe how to prepare 50 cm³ of 7.5 mg cm⁻³ solution from a 10 mg cm⁻³ stock solution of root extract using distilled water.
Click the INCORRECT step or value:
- Calculate stock volume needed: Volume_Stock = (Desired_Conc / Stock_Conc) * Final_Vol = (7.5 / 10) * 50 cm³ = 37.5 cm³.
- Measure 37.5 cm³ of the stock solution accurately.
- Mix the measured 37.5 cm³ of stock solution with 12.5 cm³ of distilled water to achieve the final volume of 50 cm³.
- Measure 7.5 cm³ of stock solution using a pipette.
- Calculate the volume of distilled water needed: Final Volume – Stock Volume = 50 cm³ – 37.5 cm³ = 12.5 cm³.
Reason Incorrect (D): The calculation in step (A) correctly shows that 37.5 cm³ of the 10 mg cm⁻³ stock solution is required to make 50 cm³ of the 7.5 mg cm⁻³ solution. Measuring only 7.5 cm³ of the stock solution (#D) would result in a final concentration of (10 mg/cm³ * 7.5 cm³) / 50 cm³ = 1.5 mg cm⁻³, which is far too dilute. Steps A, B, C, and E describe correct calculations or procedures.
Marigold plants treated with distilled water (control) had mean root length 163.0 mm. Plants treated with 10 mg cm⁻³ extract had mean root length 141.6 mm. Calculate the percentage change caused by the extract compared to the control.
Click the INCORRECT calculation method:
- Calculate percentage change: (% Change) = (Change / Original Value) * 100% = (-21.4 / 163.0) * 100% = -13.1288… %
- Calculate the absolute change in length: Final (extract) – Initial (control) = 141.6 mm – 163.0 mm = -21.4 mm.
- Round the result to 3 significant figures: -13.1 %.
- Calculate percentage change: (% Change) = (Original Value / Change) * 100% = (163.0 / -21.4) * 100%
Reason Incorrect (D): The standard formula for calculating percentage change is ((Final Value – Original Value) / Original Value) * 100%, or simply (Change / Original Value) * 100%. Step (B) correctly calculates the change (-21.4 mm). Step (A) correctly applies the formula using the change and the original (control) value (163.0 mm). Step (C) correctly rounds the result. Step (D) uses an incorrect formula, dividing the original value by the change, which does not yield the percentage change.
Suggest and explain three ways to improve confidence in the results of the investigation concerning the effect of root extract on marigold root length.
Click the suggestion LEAST likely to improve confidence or potentially reducing the scope of information:
- Improvement: Increase the number of repeats (replicate plants/containers) for each treatment group (extract concentration). Explanation: This improves the reliability of the calculated mean values and allows for better statistical analysis by reducing the impact of random variation or outliers.
- Improvement: Use genetically identical plants (e.g., clones or a highly inbred line). Explanation: This minimizes variation in root growth due to genetic differences between individual plants, making any effect of the extract clearer and more attributable to the treatment.
- Improvement: Use only two concentrations: the distilled water control and the highest extract concentration (e.g., 10 mg cm⁻³). Explanation: This simplifies the experiment design and focuses attention specifically on whether the maximum tested dose has an effect compared to no treatment.
- Improvement: Conduct appropriate statistical analysis on the collected data (e.g., calculating standard deviations/errors, performing t-tests or ANOVA). Explanation: This provides an objective assessment of whether the observed differences in root length between treatment groups are statistically significant or likely due to chance.
- Improvement: Include more intermediate concentrations of the root extract (e.g., 1, 2.5, 5, 7.5 mg cm⁻³). Explanation: This allows for a more detailed understanding of the dose-response relationship and helps identify the concentration range over which the extract has its effect, increasing confidence in the overall findings.
- Improvement: Instead of only measuring maximum root length, measure additional parameters like total root mass, total root length, or mean root length of the entire root system. Explanation: Provides a more comprehensive and potentially less variable measure of the overall impact on root growth compared to just the single longest root.
Reason Incorrect (C): While simplifying an experiment can sometimes be useful, reducing the number of concentrations to just the control and the highest (#C) would significantly limit the information gained about the dose-response relationship. It wouldn’t allow identification of potential thresholds, optimal concentrations, or non-linear effects. Using intermediate concentrations (#E), increasing replication (#A), reducing genetic variability (#B), performing statistical analysis (#D), and using more comprehensive measurements (#F) are all strategies that generally increase the confidence and robustness of the conclusions drawn from such an experiment. Focusing only on the extremes (#C) reduces the richness of the data.
To investigate the effect of the root extracts on soil microorganism diversity, soil samples were taken from the containers. State two variables that should have been standardised when taking these soil samples.
Click the factor that relates to the overall experimental setup, NOT specifically the soil sampling technique:
- The species of marigold plant used in the container.
- The same mass or volume of soil collected for each sample.
- Collecting the sample from the same depth or soil layer within each container.
- Using a standardised method for collecting, handling, and storing the soil sample to prevent contamination or changes.
- Taking the sample from a consistent position relative to the plant roots (e.g., always 5 cm from the main stem).
Reason Incorrect (A): Standardising the soil sampling procedure involves keeping the way the soil itself is collected consistent between different treatments to allow a fair comparison of the soil properties (like microbial diversity). Factors B, C, D, and E all relate directly to how the soil sample is physically obtained and handled. Factor A, the species of marigold plant, is part of the broader experimental design (related to the treatment applied via root exudates, potentially) but is not a variable standardised during the act of taking the soil sample itself.
A photomicrograph (magnification x400) shows tumour cell X. An eyepiece graticule placed over its nucleus spans 28 divisions. The calibration is 1 eyepiece graticule division = 320 nm. Calculate the actual diameter of the nucleus of cell X in µm.
Click the INCORRECT calculation step:
- Convert the final result from nm to µm: 8960 nm / 1000 nm/µm = 8.96 µm.
- Calculate the actual diameter in nm: Image diameter (in divisions) × Calibration factor (nm per division) = 28 divisions × 320 nm/division = 8960 nm.
- Calculate the actual diameter in µm directly: 28 divisions × 320 nm/division × 1000 µm/nm = 8,960,000 µm.
- Note the image diameter measured using the eyepiece graticule: 28 divisions.
- Note the calibration factor for the eyepiece graticule at this magnification: 1 division = 320 nm.
Reason Incorrect (C): Steps D and E correctly identify the measurements. Step B correctly calculates the actual diameter in nanometers (nm) by multiplying the number of divisions by the nm per division. Step A correctly converts this result from nm to micrometers (µm) by dividing by 1000 (since 1 µm = 1000 nm). Step C attempts a direct calculation but incorrectly multiplies by 1000 when converting from nm to µm, leading to a vastly incorrect answer (it should divide by 1000).
Suggest how the scientists could standardise the method of measuring the diameter of the 100 nuclei (step 5) to ensure valid comparisons between different cells or groups.
Click the option that represents a BIASED approach, not standardisation for valid comparison:
- Measure the diameter only in cells that have been stained with Haematoxylin and Eosin (H&E).
- Measure the diameter consistently at the widest visible point of each nucleus, regardless of orientation.
- Consistently measure the diameter along the shortest axis passing through the approximate centre of each nucleus.
- Consistently measure the diameter along the longest axis passing through the approximate centre of each nucleus.
Reason Incorrect (A): Standardising the measurement method means applying the exact same rule or technique to *all* nuclei being measured to ensure consistency and allow for valid comparisons between groups (e.g., benign vs. malignant, or Pap vs. H&E stained if comparing stains). Options B, C, and D describe potential consistent rules (measure widest point, shortest axis, or longest axis). Option A, however, suggests measuring *only* cells with a specific stain (H&E). If the goal was to compare H&E vs. Pap staining effects, this approach would preclude that comparison by excluding Pap-stained cells. It introduces selection bias rather than standardising the measurement technique across all samples.
Identify one variable, other than the specific method used for diameter measurement, that the scientists standardised in their procedure (steps 1-6 describing sample prep and measurement).
Click the option that represents an independent or dependent variable, NOT a standardised one:
- The type of tumour being analysed (benign or malignant).
- Blinding the observer (ensuring the scientist measuring did not know the tumour type beforehand).
- The magnification used for taking the photomicrographs and making measurements (x400).
- The final measured diameter of the nuclei obtained from the measurements.
- The number of nuclei measured per sample (e.g., 100 nuclei per tumour type).
Reason Incorrect (A or D): Standardised variables are those kept constant throughout the experiment or measurement process to ensure comparability. Blinding the observer (B), using a consistent magnification (C), and measuring a fixed number of nuclei per sample (E) are all examples of standardisation in the procedure. The type of tumour (A) is the independent variable – the groups being compared. The measured nuclear diameter (D) is the dependent variable – the outcome being measured. Both A and D are incorrect identifications of a *standardised* variable. Let’s select A.
A t-test was used to compare the mean nuclear diameter of Pap-stained cells versus H&E-stained cells. State a suitable null hypothesis for this t-test.
Click the statement that represents an ALTERNATIVE hypothesis, not a null hypothesis:
- The mean nuclear diameter of Pap-stained cells is significantly different from the mean nuclear diameter of H&E-stained cells.
- There is no significant difference between the mean nuclear diameter of the Pap-stained cells and the mean nuclear diameter of the H&E-stained cells.
- Pap staining significantly increases nuclear diameter compared to H&E staining.
Reason Incorrect (A or C): The null hypothesis (H₀) for a comparative test like the t-test always posits that there is *no* statistically significant difference or *no* effect between the groups being compared. Statement (B) correctly formulates this null hypothesis. Statements (A) and (C) both propose that there *is* a difference or effect (either non-directional in A, or directional in C). These are formulations of the alternative hypothesis (H₁), which the test seeks evidence against. Therefore, A and C are incorrect statements of the *null* hypothesis.
The t-test comparing the stains yielded a probability value p > 0.25. State the conclusion regarding the effect of the stains.
Click the INCORRECT conclusion based on the p-value:
- Conclusion: Accept the null hypothesis (or more accurately, fail to reject the null hypothesis).
- Conclusion: Reject the null hypothesis.
- Conclusion: The difference between the mean nuclear diameters measured with the two stains is statistically significant.
- Conclusion: The type of stain used (Pap or H&E) does not appear to have a statistically significant effect on the measured mean nuclear diameter in this study.
- Reasoning: The result is considered not statistically significant because the obtained p-value (p > 0.25) is greater than the conventional significance level (alpha, typically α = 0.05).
Reason Incorrect (B or C): A high p-value (like p > 0.25, which is much larger than the standard cutoff of 0.05) indicates that the observed difference between the groups is very likely to have occurred simply by random chance, assuming the null hypothesis (of no real difference) is true. Therefore, we do not have sufficient evidence to reject the null hypothesis (#A is correct interpretation, #B is incorrect). This means the difference is *not* statistically significant (#C is incorrect), and we conclude that the stain type likely does not significantly affect the measurement (#D is correct). The reasoning in #E is also correct.
Data summary: Mean nuclear diameter for 5000 benign cells = 7.3 ± 0.011 µm (SE). Mean nuclear diameter for 2400 malignant cells = 9.0 ± 0.122 µm (SE). State and explain one conclusion comparing benign and malignant cells based on this data.
Click the INCORRECT conclusion or explanation:
- Observation: On average, malignant thyroid cell nuclei (mean 9.0 µm) are larger than benign thyroid cell nuclei (mean 7.3 µm) in this dataset.
- Explanation: The observed difference in means is 1.7 µm, which appears substantial compared to the very small standard errors (SE) reported for each group (0.011 and 0.122 µm).
- Conclusion: Based on the means and standard errors, there is no significant difference in nuclear diameter between benign and malignant thyroid cells.
- Explanation: Approximate 95% confidence intervals can be estimated as Mean ± 2×SE. For benign: 7.3 ± 0.022 (7.278–7.322 µm). For malignant: 9.0 ± 0.244 (8.756–9.244 µm). These intervals do not overlap at all.
- Conclusion: The clear separation of the confidence intervals strongly suggests that the difference in mean nuclear diameter between benign and malignant cells is statistically significant.
Reason Incorrect (C): The data clearly shows a difference in mean nuclear diameter: 9.0 µm for malignant vs. 7.3 µm for benign (#A). The standard errors are very small relative to this difference (#B). As calculated in #D, the approximate 95% confidence intervals for the means do not overlap, providing strong evidence that the difference is statistically significant (#E). Therefore, concluding that there is *no* significant difference (#C) directly contradicts the presented statistical summary.
Suggest and explain two disadvantages of using this nuclear diameter measurement procedure as a routine diagnostic test for thyroid cancer.
Click the statement describing an ADVANTAGE or an INCORRECT characteristic:
- Disadvantage: Requires obtaining a tissue or cell sample (e.g., via fine-needle aspiration or biopsy), which is an invasive procedure. Explanation: Invasive procedures carry risks (bleeding, infection, pain) and cause patient discomfort or anxiety.
- Disadvantage: Non-invasive nature means results can be obtained quickly using external imaging. Explanation: Easily performed without needing tissue samples, reducing patient burden.
- Disadvantage: Measuring potentially 100 nuclei manually under a microscope is time-consuming and labour-intensive. Explanation: This limits the number of tests that can be processed, increases turnaround time, and contributes to higher costs.
- Disadvantage: Requires subjective judgment by trained personnel (pathologists/cytologists) to identify nuclei and measure diameters accurately. Explanation: This introduces potential for inter-observer variability (different people getting slightly different results) and requires specialized staff.
- Disadvantage: While means differ significantly, there might be overlap in nuclear diameters of individual benign and malignant cells, or sampling error in small biopsies. Explanation: This could potentially lead to misdiagnosis (false positives or false negatives) in some borderline cases.
Reason Incorrect (B): The procedure involves measuring cell nuclei from tissue samples obtained via methods like biopsy or fine-needle aspiration (#A). These are invasive procedures. Statement (B) incorrectly describes the method as non-invasive and performable using external imaging, which is not the case for microscopic nuclear diameter measurement. Therefore, it lists an incorrect characteristic and presents it as a disadvantage (while describing features usually considered advantages of non-invasive tests).