Mathematics and Statistics (17%)

DY0-001 · 51 questions

A home-internet provider regresses monthly bill on plan type, then adds a predictor that leaves every fitted bill unchanged, so plain R-squared stays the same and short of a perfect fit. What happens to adjusted R-squared?
A grocery chain's analyst builds a 95% confidence interval for mean basket size from a random sample of receipts. A manager says there is a 95% chance the true mean sits inside that particular interval. Which reading of the interval is right?
A factory tests whether two production lines have the same mean defect rate. The result fails to reject the null at the alpha the team chose before seeing the data. Which reading is sound?
A media company wants to test whether subscription plan, recorded as basic, plus, or premium, is associated with cancel reason, recorded as price, content, or service. Which test fits those two categorical factors?
An agency compares mean on-time minutes across four separate bus depots. On-time minutes are continuous, and the depots are independent groups. Which test fits that comparison of means?
A factory compares the mean tensile strength of fiber from two suppliers. Batches are independent, and each supplier's strengths look roughly bell-shaped. Which test fits that difference in means?
A media studio compares two forecasting models on a large sample of weekly view counts. The richer model adds several parameters and fits past weeks more closely. The studio wants the criterion that charges more per extra parameter at this large sample size. Which comparison is right?
A transit agency tests whether a new timetable changes the share of buses that arrive on time. The null hypothesis says the share is unchanged. Analysts reject that null even though the timetable truly changed nothing. Which error did they make?
A logistics desk tests whether a new dock layout changes average truck turn time. The layout truly does change turn time, but the test fails to reject the null hypothesis of no change. What error has the test made?
A precision machine shop predicts the length of a finished part in millimeters and wants an error summary in millimeters that punishes a few large misses more than many tiny ones. Which metric matches that request?
A credit-card bank chose a significance level of 0.05 before examining a test of a new late-fee policy. The test returns a p-value of 0.03. How should the team use those two numbers?
A factory model scores each part for defect risk. Leadership wants one number for how well those scores place defective parts above sound parts no matter which cutoff is later chosen on the line. Which summary matches that request?
A grants agency plots award size against review score. The cloud rises across the whole range but bends, so the relationship is monotonic and is not a straight line. Which correlation matches that shape, and which correlation is aimed at a straight line?
An auto-parts plant counts serious near-misses on one production line during each shift. Shifts are the same length, the events are uncommon, and there is no fixed number of chances inside a shift. Which distribution matches that count?
A retail loss-prevention model labels almost every transaction legitimate. Accuracy looks strong because that legitimate class supplies nearly all of the rows, yet the model rarely flags a theft. Which metric stays informative under that imbalance?
A factory quality team scores a defect flag on a counted set of parts: 40 true defect flags, 10 false defect flags, 60 missed defects, and 90 correct passes. Which pair is the precision and the recall of that defect flag?
A telecom reliability team draws larger and larger samples of repair times. One analyst says the distribution of the sample mean moves toward a normal bell. Another says the sample mean itself settles toward the population mean of repair time. Which pairing of those claims is correct?
A factory records rod diameters. The values pile up symmetrically around the mean diameter and thin out evenly on both sides, with no hard floor at zero and no long tail of rare huge readings. Which probability model matches that shape?
A factory tracks time-to-repair for equipment faults. Most jobs finish quickly, but a long right tail of rare drawn-out repairs pulls the distribution sideways. The team wants the statistic that says which tail is longer. Which description matches?
A grant-making agency plots award amounts. Most awards are small, a handful are enormous, and the histogram shows a long right tail instead of a symmetric bell. Which description matches that shape?
A streaming service emails one offer to a fixed subscriber list. Each person clicks or does not, independently, with the same chance of clicking. Analysts want a distribution for how many clicks occur in that list. Which distribution matches?
A hospital emergency department records wait time as a continuous number of minutes and records arrivals each hour as a whole-number count. Which functions match those two variables?
A utility fits a model of hourly electricity load. The residual plot is a tight band at low fitted load and a wide band at high fitted load. What is that pattern called?
A hospital compares two length-of-stay distributions that share the same mean and the same variance. One has a sharp center with thin tails, and the other has a flatter center with more extreme stays. Which statistic captures that this difference is about tail weight rather than only a peaked middle?
A utility inspected 200 transformers. Forty of them later failed. Thirty of those 40 failures had a prior hot-spot alert, and 20 of the 160 healthy units had the same alert. Using Bayes' rule on these counts, what is the probability a transformer failed given that it had shown the alert?
At a factory, a temperature sensor omits a reading more often when the true temperature is extremely high, and that high value is the one absent from the log. How should the team describe this missingness?
A logistics desk faces a delay cost of zero dollars with probability one half, 400 dollars with probability one quarter, and 800 dollars with probability one quarter. Which figure is the expected delay cost?
A bank wants the probability that a loan's loss rate lands at or below a stated cutoff, not the density sitting at that cutoff alone. Which function returns that probability directly?
A media research group has one survey sample and wants to see how much a mean rating would move if that sample had been drawn again. No new survey can be fielded. Which procedure fits?
An agency survey of benefit claimants must include a rare disability category that is only a small share of the population. A simple random draw might include none of those claimants. Which sampling method addresses that risk?
A factory engineer writes three linear equations for three machine settings and then finds that every coefficient column is a scalar multiple of the first column. The solver returns a whole line of solutions instead of one setting vector. What does that column dependence imply?
A factory engineer has two sensor locations on a flat plant-floor map and needs the straight-line separation between those points. Which distance matches that request?
A media studio places two cameras on a floor grid and wants the distance found by adding the absolute east-west gap to the absolute north-south gap. Which distance is that?
A factory calibration maps a vector of sensor readings through a square matrix. Engineers want a second matrix that undoes the map and recovers the original readings exactly. When does that inverse matrix exist?
A telecom engineer applies two different linear transforms, one after the other, to a signal feature vector. Reversing the order produces a different vector, and the engineer expected the order not to matter. Which property of matrix multiplication explains the mismatch?
A retail science team multiplies a vector of weekly category sales by a fixed matrix. One special vector comes back as a stretched copy of itself and still points the same way. What is that vector, and which property did the multiplication just show?
A retail pricing desk defines daily revenue as a function of demand alone, and demand as a function of shelf price, then needs the derivative of revenue with respect to price. Which differentiation rule builds that derivative from the two stacked functions?
An agency compares two grant-topic vectors. One document is much longer, yet the mix of topics points the same way, and the team wants a score that ignores length and compares direction. Which measure does that?
A factory scientist has a square matrix of how each production line's sensor error covaries with the others. The scientist needs one number equal to the sum of the entries on the main diagonal. Which quantity is that?
A factory yield equation depends on both kiln temperature and chamber pressure. An engineer wants the rate at which yield changes with temperature while pressure is held fixed. Which quantity is that?
A telecom analyst multiplies tower count, traffic share, and a growth ratio, all positive, and the product overflows the worksheet. The analyst takes a logarithm of that product. What does that step do to the calculation?
A bank models daily ATM cash demand. One term multiplies yesterday's demand by a coefficient, using the series' own past level rather than yesterday's forecast error. What is that term?
A factory quality diagram draws arrows from shift to a new process setting and from shift to the defect rate, plus an arrow from the setting to the defect rate. Before the team claims the setting caused the defect change, what is shift on that diagram?
A factory reliability team records vibration on the same motors every month for two years. A coworker instead wants one snapshot of every motor in the plant, taken on a single day. Which design is the monthly follow-up?
A logistics planner models weekly trailer counts that climb for months, so the mean is not stable. The analyst differences the series until that level stops drifting, then fits an ARIMA model. What did that differencing step accomplish?
An agency estimates how long job-training participants remain employed and will not assume that duration follows a named distribution such as the exponential or the Weibull. Which survival curve matches that stance?
A transit agency models daily ridership. One term adds a coefficient times yesterday's forecast error, the shock, and does not multiply yesterday's ridership level. What is that term?
A media company models how many days pass before a subscriber cancels. Many subscribers are still active on the day the extract is pulled, so their cancel time is unknown. How should those unfinished times be treated?
A telecom team has not yet launched a new hold-message script, and it can still choose who hears it. One proposal plays the new script for everyone, then compares those customers with their own prior month. Which comparison is the stronger test of the script?
A retail group gave one store a new weekend discount and left a similar store on the old prices. Sales rose at both stores, and the discounted store rose more. An analyst wants to subtract the two before-after changes and call that gap the discount's effect. What else has to be credible?
A factory will try a new coolant on some production lines and keep the current coolant on the others. Supervisors want the new coolant only on the lines that already record the fewest defects. Why should those lines be assigned by chance instead?