Exploring Two–Variable Data
What assumption must be met when using the t-distribution for constructing confidence intervals for small samples?
Population variance must be known.
The sampling method must be convenience sampling rather than random sampling.
The sample size must be greater than 30.
The population from which the sample is drawn must be approximately normally distributed.
If an initial analysis suggests there's no difference in average hours studied between students with high versus low GPAs but further investigation reveals heteroscedasticity, what conclusion can be drawn regarding potential predictors for GPA?
Study hours serve as a reliable predictor for GPA across all ranges of study time commitment.
The presence of homoscedasticity confirms a direct correlation between study times and GPAs.
Heteroscedasticity indicates that study habits do not contribute at all to predicting GPA accurately.
Variability in study hours may affect GPA prediction accuracy differently across groups.
If statisticians want to determine if there is a significant difference in means between two unrelated groups, which test should they use?
Two-sample t-test
One-sample t-test
Paired t-test
ANOVA (Analysis of Variance)
When increasing the sample size in a study, assuming all other factors are constant, how does this affect the width of a 95% confidence interval for estimating a population mean?
The effect cannot be determined without additional information.
It stays the same.
It decreases.
It increases.
When examining a histogram with a symmetric distribution shape, which measure best describes where most values fall?
Standard deviation because it measures spread irrespective of symmetry distribution shape.
Mode as it depicts only where values occur most often without symmetry relevance.
Range since it considers all values including potential outliers equally regardless of shape distribution.
Mean or median due to symmetry making them relatively equal.
Which nonparametric inferential statistic could be used to compare median revenues between two independent groups of companies when there are evident skewed distributions and outliers?
Kruskal-Wallis H test for comparing medians across more than two groups.
ANOVA to test mean differences across multiple groups.
Mann-Whitney U test (Wilcoxon rank sum test) for comparing medians between two unpaired groups.
Pearson correlation coefficient to measure strength and direction of linear relationships.
What term describes when participants are selected based on their availability or willingness to take part in research?
Voluntary Response Sampling
Quota Sampling
Judgemental Sampling
Convenience Sampling

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When comparing the center of two distributions, which of the following measures would not be affected by a few extreme outliers?
Standard deviation
Range
Mean
Median
What do we call an event consisting of all possible outcomes in an experiment?
Event collection
Outcome set
Possibility range
Sample space
In a regression analysis, if the error terms are normally distributed with mean zero but exhibit heteroscedasticity, which test would most accurately assess the significance of a predictor variable?
F-test
White's test
Durbin-Watson test
t-test