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.
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.
In a survey that asks respondents about their favorite ice cream flavor out of four choices, which measure of center would be most appropriate to report?
Standard deviation
Likert scale ratings
Mean
Median
In descriptive statistics, what do we use standard deviation to describe?
The variability or spread of a set of data points around their mean.
The exact middle value of a sorted set of numbers.
The difference between upper and lower quartiles in a dataset.
The total number count or size of our dataset.
Given distribution skewness and leptokurtosis, how might transformations techniques promote normalcy assumptions underpinning parametric inferential statistics?
Adding or subtracting a constant to each datum to shift location, not shape of the distribution
Raising data values to the second power or square root to transform
Applying Box-Cox power transformations to reduce skewness and kurtosis
Utilizing bootstrapping methods to generate numerous resamples of the original dataset
If a random sample of size 40 is taken from a population, under what condition would the distribution of the sample mean be approximately normal?
There are outliers present in the population.
The population distribution is skewed to the right.
The sample size is less than 30.
The population is normally distributed.
Which graphical representation would generally be used for displaying frequency distribution of one categorical variable?
Scatterplot
Boxplot
Bar chart
Histogram

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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.
What statistic could help understand how much individual test scores deviate from an average test score?
Variance.
Range.
Standard deviation.
Mean absolute deviation (MAD).
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