Statistics for Data Analysis final test: 25 free questions

Q1 / 25

A team wants to detect either an increase or a decrease from a target. How should it write the alternative?

1. ARejecting the null proves the proposed scientific mechanism with certainty.
2. BA two-sided research question requires a two-sided alternative, such as a parameter not equal to its null value.
3. CThe significance level is a description of the observed effect size. That would make alpha = 0.05 describe a five-percent effect instead of a long-run false-rejection rate.
4. DA p-value above alpha means the null model has been verified as true.

Q2 / 25

Spearman correlation between x and y is 0.85. The analyst then replaces y by its negative, a strictly decreasing transformation. What happens to the Spearman correlation?

1. AIt stays at 0.85, because any strictly monotonic transformation leaves rank association unchanged.
2. BIt becomes -0.15, because the transformation rescales the coefficient as well as reversing it.
3. CIt drops to 0, because negating one variable destroys the monotonic relationship between them.
4. DIt becomes -0.85, because reversing the ranks of one variable flips the sign but not the strength.

Q3 / 25

What generally happens to the standard error when independent sample size increases?

1. AIncreasing independent sample size generally reduces the standard error of a mean when the sampling assumptions remain valid.
2. BIt means the estimator is unbiased and the sample frame is fully representative of the target population, regardless of design.
3. COnly the numerical value of the sample mean determines its standard error.
4. DFor an independent mean, standard error grows with sample size and shrinks when outcome variability increases for every estimator and sampling design.

Q4 / 25

Why is outcome support an early filter when choosing among normal, binomial, and Poisson models?

1. ADistribution choice must respect the support of the outcome, such as real-valued measurements versus nonnegative counts.
2. BRecording a seed proves that the chosen distribution matches the real data-generating process.
3. CSupport can be ignored until after model fitting.
4. DAny count should use a normal model if its histogram is symmetric, even when negative values receive material probability under the fit.

Q5 / 25

What comparison creates Pearson's chi-square statistic?

1. AThe chi-square statistic aggregates squared observed-minus-expected differences scaled by their expected counts.
2. BBonferroni multiplies the family alpha by the number of tests for each comparison.
3. CExpected counts are copied directly from the largest observed row.
4. DA chi-square independence test compares the means of two quantitative variables.

Q6 / 25

Why does covariance change when measurement units change?

1. ACovariance is expressed in the product of the variables' units and is therefore scale dependent.
2. BA zero Pearson correlation establishes statistical independence. It mistakes absence of linear correlation for absence of nonlinear dependence.
3. CCovariance is unitless and constrained between minus one and one.
4. DThe coefficient alone reveals clusters and influential observations in the scatterplot.

Q7 / 25

How can a NumPy pseudorandom sequence be made repeatable?

1. AConstruct a Generator from an explicit seed
2. BReplace the generator with the system clock
3. CCall the default generator without any seed
4. DDraw a fresh, unrecorded operating-system seed before each draw

Q8 / 25

What autocorrelation pattern is expected for random data?

1. ARandom data should have autocorrelations near zero, apart from sampling variation.
2. BA lag plot compares the sample mean with the median instead of pairing observations separated in order.
3. CIgnoring positive dependence makes standard errors wider because correlated observations add more independent evidence.
4. DNear-zero sample autocorrelations prove complete randomness and exclude every other form of non-random structure.

Q9 / 25

What must connect the target population, operational frame, and selected units before generalizing the result?

1. ACoverage bias disappears once most listed units respond, even if an entire region is absent from the list and the sample remains very large.
2. BInference to a target population requires a defensible link between that population, the sampling frame, and the selection process.
3. CNothing learned from a sample can describe a population under any design, because only a census permits inference.
4. DA sample fact is automatically a population fact whenever the sample contains more than one thousand units.

Q10 / 25

A 95% interval comes from a convenience sample with a skewed outcome, and the method's assumptions are undocumented. What limits its interpretation?

1. AA sufficiently narrow interval repairs any lack of representation in the convenience sample.
2. BSkewness and selection affect only the point estimate, never the interval procedure.
3. CInterval interpretation depends on the assumptions and sampling process used to construct the interval.
4. DThe 95% label alone guarantees the stated coverage for every sampling design and outcome shape.

Q11 / 25

What does the cumulative distribution at 30 minutes mean?

1. AThe 90th percentile is a probability of 90 attached to one outcome.
2. BThe cumulative distribution at x gives the density height at x.
3. CIt returns a value whose cumulative probability reaches x, so its input is a probability rather than an outcome threshold.
4. DThe cumulative distribution function at a value gives the probability that the random variable is less than or equal to that value.

Q12 / 25

Residuals drift over collection order and the deadline prevents new data collection. What must happen before the original inferential conclusion is trusted?

1. APower is the probability that the null hypothesis is true after observing the data.
2. BWhen residual diagnostics contradict model assumptions, the model or inferential method should be revised and checked again.
3. CA residual funnel confirms that the error variance is constant.
4. DA Type I error means failing to reject a false null hypothesis.

Q13 / 25

A probability sample is drawn from the customer registry. Which inferential reach is supplied by that operation?

1. ARandom sampling supports generalization from the sample to the population represented by the sampling process.
2. BDifferent subgroup patterns should be hidden behind the pooled estimate. It suppresses heterogeneity needed to interpret the pooled coefficient.
3. CAn aggregate coefficient is unchanged by subgroup composition.
4. DA strong observational correlation establishes the direction of causation.

Q14 / 25

What model information should accompany an estimate?

1. AA statistical claim should name the relevant assumptions, diagnostics, and uncertainty rather than report the estimate alone.
2. BA precise estimate from a convenience sample automatically represents the entire target population.
3. CMissing observations affect precision but cannot change which population is represented. It ignores that observed cases may represent a systematically different subset.
4. DA significant result is practically important regardless of effect magnitude.

Q15 / 25

How does the Mann-Whitney U procedure use two samples?

1. AIt compares only the two arithmetic means
2. BIt assumes every observation has an identical numerical value
3. CIt pairs observations by their row positions
4. DIt ranks their combined observations and compares rank sums

Q16 / 25

Which design factors jointly determine the precision of an estimate?

1. ARepeated readings never add information of any kind, even about measurement repeatability.
2. BRandomization cannot protect against time trends, because treatment order has no connection to systematic measurement drift.
3. CTen repeat readings of one item add exactly as much information about between-item variation as one reading from ten independently produced items.
4. DPrecision depends on inherent variability, measurement error, independent replication, and the efficiency of the sampling scheme.

Q17 / 25

Why should a confidence interval be reported instead of reducing estimation to a binary label?

1. AAn interval estimate lists the central observations in the sample.
2. BA confidence interval communicates uncertainty in an estimate rather than replacing the estimate with a binary decision.
3. CIt gives the fixed parameter a 95 percent chance of moving into the already observed interval.
4. DIt replaces the point estimate with a binary significant/not-significant label.

Q18 / 25

What information is supplied by a probability distribution for that payoff?

1. AA random variable is the unordered list of outcomes that happened to appear in one sample, and it may assign a different number to the same outcome after data collection.
2. BIt assigns probabilities to intervals only and always gives zero probability to every individual discrete value.
3. CA random variable is a probability assigned to an event rather than a numerical value assigned to each possible outcome.
4. DA probability distribution describes possible values of a random variable and how probability is allocated across those values.

Q19 / 25

Twenty independent tests of true null hypotheses are each run at the same per-test alpha. What happens to the chance of at least one false rejection?

1. ABonferroni multiplies the family alpha by the number of tests for each comparison.
2. BWith independent tests of true null hypotheses, an unchanged per-test threshold increases the chance of at least one false rejection.
3. CExpected counts are copied directly from the largest observed row.
4. DTesting more null hypotheses leaves the family-wise false-positive chance unchanged. It ignores additional opportunities to reject a true null by chance.

Q20 / 25

What can an observational association establish without random assignment?

1. AA strong observational correlation establishes the direction of causation.
2. BAn aggregate coefficient is unchanged by subgroup composition. It ignores how subgroup weights can alter or reverse a pooled association.
3. CWithout random assignment, an observed relationship supports association but does not by itself establish causation.
4. DRandom sampling and random assignment provide the same inferential guarantee.

Q21 / 25

A monthly report is produced by running notebook cells manually, applying an undocumented spreadsheet correction, and using globally installed packages. Which redesign most improves reproducibility?

1. AVersion the pipeline, manual fix, code, and environment
2. BRecord only the final package count and report value
3. CAsk one analyst to memorize the cell order and correction
4. DKeep the notebook unchanged and add more screenshots

Q22 / 25

What should determine whether a rank-based method is appropriate?

1. AThe target, design, data, and method assumptions
2. BThe method that produces the smallest p-value
3. CThe option listed first by statistical software
4. DA universal preference for nonparametric labels

Q23 / 25

Which summaries naturally match a product category and which match a measured weight?

1. AA proportion may validly be modeled below zero or above one if the fitted curve is smooth, and a count may take negative fitted values without qualification.
2. BFrequencies are sufficient for every quantitative variable, even when magnitude and dispersion are the substantive targets of the analysis.
3. CMeans and standard deviations are the natural summaries for unordered category labels.
4. DMeans and standard deviations require quantitative meaning; frequencies and proportions are natural summaries for categorical variables.

Q24 / 25

A report states only “SE = 2” for clustered data, without naming the estimator, units, or design. What is needed before that number has a clear interpretation?

1. AIts units and assumptions do not matter once a numerical value is reported.
2. BIt is the distribution of all population values and remains unrelated to the estimator or sampling process under any estimator.
3. CA reported standard error is meaningful only relative to a specified estimator and a defensible sampling or model process.
4. DA standard error is self-explanatory without naming the estimator.

Q25 / 25

With eight ordered observations, which positions determine the median?

1. AStandard deviation is the average unsquared deviation from the median.
2. BMean and median react identically to an arbitrarily extreme observation, so neither offers greater robustness for skewed data.
3. CWith eight ordered observations the median sits between the fourth and fifth values, the two central positions.
4. DThe mean is determined only by the two middle ranks, while the median uses every magnitude and therefore moves farther when one extreme value changes.