QCAA General Mathematics Bivariate data analysis 1

A negative association requires a correlation coefficient less than zero ($r < 0$), but the given value is $0.23$.

A strong positive association typically corresponds to an $r$ value closer to $1$ (e.g., $r > 0.7$), whereas $0.23$ represents a weak relationship.

This option describes a correlation coefficient close to $-1$, but the given value is positive and indicates a weak relationship.

Neither variable asks for a specific numerical measurement, such as an exact dollar amount. Since the responses are groups or labels, they are not numerical variables.

While payment preference is categorical, budget preference is also categorical because it groups responses into ranges ('less than ＄50' or 'more than ＄50') rather than asking for an exact numerical value.

Payment preference ('cash' or 'electronic') is clearly a categorical variable, not numerical. Budget preference is also categorical, making this option entirely incorrect.

While the equation represents a linear relationship, a correlation coefficient of 0.92 indicates a strong association, not a weak one.

The equation $y = 4.6x - 35$ represents a linear relationship, and a correlation coefficient of 0.92 indicates a strong association, making both parts of this description incorrect.

Although the association is strong, the equation $y = 4.6x - 35$ is in the form $y = mx + c$, which models a linear relationship, not a non-linear one.

This is an example of univariate data because it involves only one variable (the rating) for each observation.

This is univariate data because it records only a single variable (the count of cars) at a specific location.

This is univariate data because it measures only one variable (time spent) for each person observed.

This reverses the variables; $R^2$ measures the proportion of variation in the response variable ($y$) explained by the explanatory variable ($x$), not the variation in $x$ explained by $y$.

$R^2$ measures the proportion of the variation in the observed response values ($y$), not the predicted outcomes, that is explained by the model.

This refers to the variation in the explanatory variable ($x$), whereas $R^2$ specifically measures the explained variation in the response variable ($y$).

These are typically treated as two categorical variables associated with a car, rather than a clear explanatory variable driving a response variable.

This example describes an association between a category and a summary statistic, rather than a direct explanatory-response relationship between variables.

This option lists the response variable (plant growth) first and the explanatory variable (amount of fertiliser) second, which is the reverse of the order requested.

This option describes the marginal percentage of all students who passed Electrical. The table provides conditional percentages based on Machinery results, not the total population distribution.

This option describes the marginal percentage of all students who failed Machinery. The value 10% represents a specific intersection of results relative to a subgroup, not the total proportion of students failing Machinery.

This interprets the condition in reverse (conditioning on the row). Since the rows do not sum to 100% ($80\% + 10\% \neq 100\%$), the percentages are not based on the group of students who achieved satisfactory in Electrical.

This is simply the raw count of field athletes who prefer brand Y (12). To find the percentage, you must divide this count by the total number of field athletes.

This represents the percentage of the total population (80 athletes) who are field athletes preferring brand Y ($\frac{12}{80} = 15\%$). The question asks specifically for the percentage of field athletes.

This calculates the percentage of athletes preferring brand Y who are field athletes ($\frac{12}{30} = 40\%$). You used the column total (Total preferring Y) as the denominator instead of the row total (Total Field athletes).

Correlation does not imply causation. While there is a statistical association, we cannot conclude that spending less time on social media directly causes an increase in test performance.

This describes a positive association, where both variables increase together. The problem explicitly states there is a negative association.

This option incorrectly assumes causation. A negative association only shows a relationship between the variables, not that one causes a change in the other.

This describes a positive association, where both variables decrease together. A negative association means they move in opposite directions.

This represents the percentage of students who preferred comedy and were in Year 7–8 ($\frac{20}{80} = 25\%$), rather than those in Year 9 or higher.

This calculation only includes students in Year 9–10 ($\frac{24}{80} = 30\%$) and neglects to include the Year 11–12 students who are also part of the "Year 9 or higher" group.

This is the raw count of students in Year 9 or higher who preferred comedy ($24 + 36 = 60$), not the percentage relative to the total number of students who preferred comedy.

Vehicle age is the explanatory variable because it predicts the distance travelled, not the response variable.

Response variables are plotted on the vertical axis ($y$-axis), not the horizontal axis.

Distance travelled is the response (dependent) variable because it depends on the age of the vehicle, not the explanatory variable.

This is the raw count of students who drive (12), not the percentage. To find the percentage, you must divide this count by the total number of students.

This value represents the percentage of the entire sample (staff and students combined) who are students driving their own car ($\frac{12}{80} = 15\%$), rather than the percentage of just the student group.

This figure represents the percentage of all drivers who are students ($\frac{12}{30} = 40\%$), rather than the percentage of students who drive.