Exploring Two–Variable Data
Which measure helps determine if there is an association between two categorical variables in a contingency table?
Slope of regression line
Chi-square test statistic
Sample mean difference
Correlation coefficient
What does it mean if two categorical variables are independent?
There exists no statistical relationship measurable by numerical means.
The sum total counts across categories remains constant within both variables.
One variable causes changes in another variable.
The distribution of one variable is not affected by the distribution of another variable.
In analyzing data from a school election, if you want to determine whether grade level and candidate choice are associated with each other without regard to actual vote counts, which measure would be most appropriate?
Chi-square test for independence
Simple linear regression analysis
T-test comparing means across groups
Z-score comparison between groups
If an observational study observes that there is an association between eating breakfast and high school GPA scores through a logistic regression model, what potential issue should be considered before concluding causation?
The regression coefficient could be zero
The sample size may be too small to detect an effect
Confounding variables may exist
Random assignment was not used in groups
After analyzing data from two categorical variables using a logistic regression model, researchers find an odds ratio of 0.7 between variable A and B. However, how significant should this result be considered if the sample was non-randomly selected?
Sample ethnicity has no bearing on sampling methods
Selection bias may not exist in sampling
Random sampling ensures generalizability across study groups
Non-generalizable to the wider population due to non-random sampling
When analyzing the relationship between two categorical variables using a two-way table, what measure should be calculated to compare the distributions across categories?
Sample proportions
Joint relative frequencies
Conditional relative frequencies
Marginal relative frequencies
What type of relative frequency does the question "What is the probability of choosing someone that is a girl and likes ice cream" yield?
Conditional relative frequency
Joint relative frequency
Cumulative relative frequency
Marginal relative frequency

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To explore if there's an interaction between studying habits and academic performance, which graphical representation should be used to display counts from a survey conducted on students?
A segmented bar chart with percentages stacked by study habit categories for each level of academic performance
A histogram displaying distribution frequency of study hours binned together across all levels of performance
A pie chart depicting proportionate representation of study habits among students with high academic performance only
A line graph showing change in study habits over time grouped by academic performance levels
What is a plausible reason for finding a positive correlation between ice cream sales and drowning incidents without implying causation?
Both ice cream sales and drowning incidents increase during summer months due to warmer weather.
Drowning incidents cause an increase in ice cream sales.
Eating ice cream causes people to drown.
People who are prone to drowning prefer eating more ice cream.
Which type of variable cannot be meaningfully ordered or measured on a continuous scale?
Categorical variable
Quantitative variable
Conditional variable
Independent variable