- Specification route
- MS
- Question bank
- 10 questions
- Course stage
- AS / Year 12
Sample questions
A researcher wishes to determine if there is a significant difference between the mean lengths of leaves from oak trees growing in a shaded wood compared to those growing in an open field. Which statistical test should they use?
Show clue
This test is specifically designed to compare the mean values of two sets of normally distributed data.
Show answer and explanation
Answer: Student's t-test
Mathematical Skills (MS 1.9). The Student's t-test is used to compare the means of two different samples to see if the difference between them is statistically significant.
An ecologist collects data on the concentration of nitrates in the soil and the corresponding biomass of a plant species at various sites. Which statistical test should be used to see if these two variables are related?
Show clue
This test looks for an association or relationship between two continuous variables.
Show answer and explanation
Answer: Spearman's rank correlation coefficient
Mathematical Skills (MS 1.9). Spearman's rank correlation coefficient is used to determine if there is a significant correlation (positive or negative) between two continuous variables.
When performing a statistical test, a student calculates a probability ($p$) value of $p < 0.05$. What is the correct conclusion to draw from this result?
Show clue
In biology, a $p$ value of less than 0.05 ($5\%$) is the standard threshold for statistical significance.
Show answer and explanation
Answer: Reject the null hypothesis; there is a less than $5\%$ probability that the difference or correlation observed is due to chance.
MS 1.9. If $p < 0.05$, the probability that the results occurred purely by chance is less than $5\%$. This is deemed statistically significant, so the null hypothesis is rejected.
A strong positive correlation is found between the sales of ice cream and the number of shark attacks in a coastal town. What biological principle must be remembered when interpreting this data?
Show clue
Just because two things happen at the same time doesn't mean one causes the other.
Show answer and explanation
Answer: Correlation does not equal causation; both variables may be influenced by a third independent factor, such as high temperature.
MS 1.9. A significant correlation only indicates that two variables change together. It does not prove a causal mechanism, as a third variable (e.g., hot weather driving people to the beach and making them buy ice cream) might cause both.
When plotting the growth of a bacterial population over several days, why might a scientist choose to use a logarithmic scale ($log_{10}$) for the y-axis (number of bacteria)?
Show clue
If a population goes from $10$ to $10,000,000,000$, plotting it on standard graph paper is physically impossible.
Show answer and explanation
Answer: Because bacterial populations grow exponentially, a logarithmic scale allows a massive range of values to be plotted clearly on a single graph.
Mathematical Skills (MS 3.3). Logarithmic scales are used when data covers a vast range of magnitudes, such as the exponential growth of microorganisms, condensing exponential curves into straight, readable lines.
A student plots a curve showing the volume of product formed over time in an enzyme reaction. How can they calculate the exact rate of reaction at precisely $30$ seconds?
Show clue
The rate at a specific instant is the steepness of the curve at that exact point.
Show answer and explanation
Answer: Draw a straight tangent line to the curve at the $30$-second mark and calculate the gradient of that tangent ($\Delta y / \Delta x$).
Mathematical Skills (MS 3.6). To find the rate at a specific point on a curve, you must draw a tangent (a straight line touching the curve at that point) and calculate its gradient.
A measuring cylinder has scale divisions of $2\ cm^3$. What is the absolute uncertainty of a single measurement taken with this instrument?
Show clue
For an analogue scale, the uncertainty is generally half of the smallest scale division.
Show answer and explanation
Answer: $\pm 1\ cm^3$
MS 1.11. The absolute uncertainty of a single reading on an analogue scale is half the smallest division. Since the smallest division is $2\ cm^3$, the uncertainty is $\pm 1\ cm^3$.
A student measures $10\ cm^3$ of solution using a pipette with an uncertainty of $\pm 0.1\ cm^3$. What is the percentage error of this measurement?
Show clue
Percentage error = (Absolute uncertainty / Measured value) $\times$ 100.
Show answer and explanation
Answer: $1\%$
MS 1.11. Percentage error is calculated as $(0.1 / 10) \times 100 = 1\%$.
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