Mathematics and Statistics
Free CompTIA DataX practice — 6 questions on Mathematics and Statistics, with explanations. No sign-up. Full 12-question mixed test →
A data science team runs a one-way ANOVA comparing average time-on-page across four redesigned landing page variants (A, B, C, D). The ANOVA F-test returns p = 0.008, rejecting the null hypothesis of equal means. The team must now determine exactly which pairs of variants differ significantly while controlling the family-wise error rate. Which approach BEST accomplishes this?
Tukey's HSD test is specifically designed for pairwise mean comparisons after a significant ANOVA result, and it controls the family-wise error rate across all comparisons simultaneously.
A reliability engineer is modeling the number of hard-drive failures that occur in a data center per week. Failures are rare, independent, and occur at a constant average rate. Which probability distribution is MOST appropriate to model this count data?
The Poisson distribution models the number of rare, independent events occurring within a fixed interval at a constant average rate, which exactly matches this failure-count scenario.
A researcher builds a contingency table to test independence between customer region (4 categories) and product preference (5 categories) using a chi-squared test of independence. How many degrees of freedom does this test have?
Degrees of freedom for a chi-squared test of independence equal (rows - 1) x (columns - 1) = (4-1) x (5-1) = 3 x 4 = 12.
A data scientist computes a 95% credible interval for a parameter using a Bayesian posterior distribution, and a colleague computes a 95% confidence interval for the same parameter using frequentist methods. Which statement correctly distinguishes the interpretation of these two intervals?
This correctly captures the fundamental distinction: the Bayesian credible interval is a direct probability statement about the parameter conditioned on the data and prior, while the frequentist confidence interval is a statement about the long-run behavior of the interval-construction procedure across repeated sampling.
An analyst wants to fit an ARIMA model to a company's monthly revenue time series, which shows a clear upward trend over five years. Before selecting model parameters, which step should be performed FIRST to ensure valid results?
ARIMA modeling requires stationary input data. The ADF test checks for the presence of a unit root, and if the series is found non-stationary due to trend, differencing is the standard correction before proceeding to model fitting.
While training a regression model using gradient descent, the analyst observes that the loss value oscillates wildly and diverges to increasingly large values after each iteration instead of decreasing. Which adjustment is MOST likely to resolve this issue?
Oscillating, diverging loss during gradient descent is a classic symptom of an excessively large learning rate causing the optimizer to overshoot the minimum on each step. Reducing the learning rate produces smaller, more stable update steps that allow convergence.
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