Exploring Two–Variable Data
When analyzing bivariate categorical data, which visual representation is useful for showing the relationship between two categorical variables and comparing proportions of data points in different categories?
Mosaic plot
Frequency chart
Histogram
Scatterplot
When a linear regression model is applied to a set of data, which of the following conditions, if violated, suggests that the model may not be robust for making predictions?
The scatterplot of residuals versus fitted values shows a clear pattern.
The variance of the residuals is constant across all levels of the independent variable.
The scatterplot of residuals versus predictor variables is random without discernible pattern.
The quantile-quantile (Q-Q) plot of residuals follows roughly a straight line.
What are the primary reasons researchers use stratified sampling?
To ensure representation of subgroups within a population
Avoiding contact with hard-to-reach subjects
Increase chances of selecting rare outcomes
Underrepresent certain segments for cost savings
If a data set has a mean of 50 and a standard deviation of 5, which value would most likely be considered an outlier?
45
70
55
50
What kind of sample is likely to be biased if individuals volunteer themselves to participate in a survey?
Simple Random Sample
Stratified Random Sample
Cluster Sample
Voluntary response sample
A basketball coach recorded both the number of points scored and minutes played by each player in last season's games; what type of analysis can help understand if there's an association between these two variables?
T-test for mean difference
ANOVA (Analysis of Variance)
Chi-square test for independence
Correlation coefficient calculation
What is the purpose of analyzing bivariate categorical data?
To determine if there is a statistically significant relationship between two variables
To quantify the strength and direction of the relationship between two variables
To visualize the relationship between two quantitative variables
To compare proportions of data points in different categories

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What type of variable can only take on specific numerical values often counting something such as students in a classroom?
Continuous variable
Ratio
Interval
Discrete variable
If an AP Statistics student wants to determine whether there's an association between hours studied and exam performance, which method should they use assuming both variables are quantitative?
Histogram analysis
Two-way table and chi-square test
Scatterplot and correlation coefficient calculation
Boxplots comparison
What type of data can be represented by a bar chart showing the frequency or count of data points in different categories?
Quantitative data
Bivariate categorical data
Categorical data
Bivariate quantitative data