Probability, Random Variables, and Probability Distributions
How should one interpret a strong positive correlation between consumption of whole grains and overall health in adults from an observational study?
Adults with better health are causing an increase in the consumption of whole grains within populations studied.
There may be confounding factors such as lifestyle choices influencing both whole grain consumption and health outcomes.
Eating more whole grains directly causes improvements in adult health outcomes across populations studied.
The observed positive correlation must be due solely to chance rather than any actual association between variables.
Which graphical representation would generally be used for displaying frequency distribution of one categorical variable?
Scatterplot
Boxplot
Bar chart
Histogram
What statistic could help understand how much individual test scores deviate from an average test score?
Variance.
Range.
Standard deviation.
Mean absolute deviation (MAD).
What is the probability of flipping a fair coin and it landing on heads?
0.75
0.5
0.25
1
In an experiment designed to study the effect of light on plant growth, what type of analysis would best allow statisticians to consider both the intensity and duration of light as factors affecting plant height?
Linear regression
Two-way ANOVA (Analysis of Variance)
Pearson's Correlation Coefficient analysis
One-way ANOVA
What can be concluded if a set of data has a low standard deviation?
The mean of the dataset is significantly higher than the median.
The data points are closely clustered around the mean.
There is a high likelihood that outliers exist in the dataset.
The data points are widely spread out from the mean.
When testing the significance of a linear regression model between hours studied and test scores, which condition if violated would most likely reduce the validity of the regression analysis?
Equality of variances for different amounts of study time.
Normal distribution of test scores for each amount of study time.
Random selection of students' data points included in the study.
Linearity of the relationship between hours studied and test scores.

How are we doing?
Give us your feedback and let us know how we can improve
A scatterplot showing residuals versus fitted values in a simple linear regression should ideally display what pattern to satisfy assumptions necessary for inference?
A clear positive or negative trend indicating predictability in errors.
A parabolic shape suggesting a quadratic relationship exists.
No discernible pattern, with residuals scattered randomly around zero.
Clustering of residuals at high and low ends indicative of homoscedasticity.
If you roll a standard six-sided die, what is the probability of rolling an even number?
1/2
2/3
3/4
1/6
In statistical analysis, random patterns occur when:
The data variations are not systematic and cannot be predicted with any degree of certainty.
There is an error
The data variations are always biased.
The data variations are systematic and can be predicted with some degree of certainty.