4. Statistical Inference and Evidence-Based Decisions

Introduction: From Observed Data to Defensible Decisions

Quality management depends on decisions made under uncertainty. A production team may observe that the average fill volume has changed, a hospital may wish to know whether a revised handover process reduces errors, or a service organization may compare customer-waiting times before and after process redesign. In each situation, the available data represent only a limited set of observations, while the decision concerns a broader and usually unobserved process.

Statistical inference provides the disciplined methods required to move from sample evidence to conclusions about a population or process. It does not eliminate uncertainty. Rather, it measures and communicates uncertainty so that managers can distinguish a meaningful signal from ordinary variation. This distinction is central to Total Quality Management (TQM), where improvement decisions should be based on evidence rather than anecdote, intuition, or isolated observations.

Descriptive statistics summarize what has been observed. Inferential statistics address what may reasonably be concluded beyond the observations. The principal tools are sampling, estimation, confidence intervals, hypothesis tests, effect sizes, and power analysis. Used together, they support decisions that are statistically credible and operationally useful. Used mechanically, they can produce misleading conclusions, unnecessary process changes, or failure to detect important quality problems.

Learning Objectives

After studying this chapter, the reader should be able to:

1. Distinguish populations, samples, parameters, statistics, and sampling distributions.

2. Explain how sampling design affects the credibility of quality evidence.

3. Construct and interpret confidence intervals for common quality measures.

4. Formulate and evaluate null and alternative hypotheses.

5. Interpret p-values without confusing them with practical importance.

6. Explain Type I error, Type II error, statistical power, and decision consequences.

7. Select and interpret appropriate effect-size measures.

8. Recognize common statistical misinterpretations and sources of bias.

9. Integrate statistical significance, practical significance, process knowledge, and risk into quality decisions.

10. Apply inferential methods to a realistic quality-improvement case.

The Inferential Perspective in Quality Analytics

A population is the complete set of units, transactions, products, patients, or time periods to which a conclusion is intended to apply. A sample is a subset of that population. A population parameter, such as the true mean defect rate, is generally unknown. A sample statistic, such as the observed mean defect rate, is calculated from the data and used to estimate the parameter.

The quality analyst must first define the population carefully. “All products” may mean all products manufactured on one line during a shift, all products made at a plant during a quarter, or all products sold across several facilities. A conclusion is only as broad as the sampling frame and study design permit. If data are collected only during the day shift, conclusions about night-shift performance require justification. If only complaints are analyzed, the data do not represent all customers because satisfied or silent customers are excluded.

Sampling and Representativeness

Sampling is not merely a way to reduce data-collection cost. It determines whether the evidence can support generalization. In a simple random sample, every population unit has a known and equal probability of selection. A systematic sample selects every kth unit after a random starting point. Stratified sampling divides the population into relevant groups and samples within each group; this is useful when quality differs by product family, supplier, region, or shift. Cluster sampling selects naturally occurring groups, such as branches or production lots, and then studies units within those groups.

Convenience samples are easy to obtain but often vulnerable to selection bias. A quality team that studies only products available at the inspection station may miss failures occurring during transport. A voluntary customer survey may overrepresent unusually satisfied or dissatisfied respondents. Time-related patterns also matter. Sampling at fixed intervals can inadvertently coincide with cycles in staffing, machine temperature, demand, or replenishment.

For process data, independence requires particular attention. Consecutive observations may be correlated because they share the same machine condition, operator, batch, or environmental setting. Treating correlated observations as independent can make the apparent amount of information much larger than it really is and can produce confidence intervals that are too narrow.

Sampling Distributions and the Central Limit Idea

If repeated samples of equal size are drawn from a population, their statistics vary. The distribution of a statistic across repeated samples is its sampling distribution. For a sample mean, the standard deviation of this distribution is the standard error. When observations are independent and the population standard deviation is σ, the standard error of the mean is approximately σ divided by the square root of n. Since σ is usually unknown, the sample standard deviation is used as an estimate.

The central limit theorem explains why the sampling distribution of a mean often becomes approximately normal as sample size increases, even when individual observations are not normally distributed. It does not state that the raw data become normal, nor does it guarantee reliable inference for every sample size. Strong skewness, extreme outliers, dependence, or a highly unusual sampling design may require transformations, robust methods, or nonparametric procedures.

Estimation: Quantifying What the Data Suggest

A point estimate gives a single best estimate of a population parameter. For example, if 18 of 600 inspected units are defective, the sample defect proportion is 18/600, or 0.03. Although the point estimate is useful, it does not reveal how precisely the sample estimates the population. A confidence interval supplements the point estimate by presenting a range of values compatible with the data and a stated confidence level.

Confidence Intervals

For a mean, a commonly used interval is:

sample mean ± critical value × standard error

When the population standard deviation is unknown, the t-distribution is generally used, particularly for smaller samples. For a proportion, an interval is constructed using the estimated proportion and its standard error, although special methods are preferable when the sample is small or the proportion is near zero or one.

A 95% confidence interval should not be interpreted as saying that there is a 95% probability that the fixed population parameter lies within this particular calculated interval. Under repeated sampling from the same population using the same method, approximately 95% of intervals constructed by the method would contain the parameter. In practical communication, it is reasonable to say that the interval provides a range of values supported by the data at the 95% confidence level, provided the assumptions and sampling design are credible.

For example, suppose a service centre observes an average waiting time of 14.2 minutes and obtains a 95% confidence interval from 13.4 to 15.0 minutes. The interval indicates both the estimated level and its precision. If the organization has set a target of no more than 15 minutes, the evidence is consistent with a process whose average is below the target, but the upper endpoint also indicates that the true average could be close to the limit. A decision-maker may therefore require continued monitoring rather than declare the issue permanently resolved.

Interval width is affected by sample size, variability, and confidence level. Larger samples generally produce narrower intervals, while greater process variation produces wider intervals. Raising the confidence level from 95% to 99% produces a wider interval because greater coverage requires a larger margin of error. A narrow interval is not automatically accurate: systematic bias can produce a precise estimate of the wrong quantity.

Intervals for Differences

Quality decisions often compare two conditions. The relevant estimate may be the difference in means, the difference in defect proportions, or a ratio such as a relative risk. A confidence interval for a difference is especially informative. If a 95% interval for the improvement in average cycle time is from 1.2 to 3.8 minutes, the direction and plausible magnitude of improvement are clearer than they would be from a p-value alone.

When a confidence interval for a difference includes zero, a difference cannot be established at the corresponding two-sided significance level. However, this does not prove that the two processes are identical. The interval may include both a small benefit and a small disadvantage because the study lacks precision. Equivalence or non-inferiority questions require specifically designed hypotheses and decision margins rather than a simple failure to obtain statistical significance.

Hypothesis Testing as a Structured Argument

Hypothesis testing begins with a claim about a population parameter. The null hypothesis, denoted H₀, usually represents no change, no difference, or a specified reference condition. The alternative hypothesis, H₁ or Hₐ, represents the effect or departure that the investigation seeks to detect.

Suppose a filling machine is specified to produce a mean volume of 500 millilitres. A two-sided test might state H₀: μ = 500 and Hₐ: μ ≠ 500. If only underfilling creates a regulatory or customer risk, a one-sided alternative Hₐ: μ < 500 may be appropriate. The direction must be established before examining the results; changing from a two-sided to a one-sided test after seeing the data increases the risk of a misleading conclusion.

A test statistic measures how far the sample result is from the null value relative to its standard error. The p-value is the probability, assuming the null hypothesis and model assumptions are true, of obtaining a result at least as extreme as the observed result in the relevant direction. It is not the probability that the null hypothesis is true, nor is it the probability that the result occurred by chance in a general, non-technical sense.

The analyst compares the p-value with a pre-specified significance level, α, commonly 0.05. If p ≤ α, the result is described as statistically significant and the null hypothesis is rejected. If p > α, the null hypothesis is not rejected. “Not rejected” is preferable to “accepted,” because the evidence may simply be insufficient to distinguish the null value from plausible alternatives.

Statistical significance depends on effect size, variability, and sample size. A very small and operationally irrelevant difference can have a very small p-value in a large database. Conversely, a substantial improvement may fail to reach significance in a small or highly variable study. Consequently, a p-value should normally be reported with an effect estimate, confidence interval, sample size, and process context.

Paired and Independent Comparisons

The choice of test must reflect the design. In a before-and-after study in which the same machines, employees, or cases are measured twice, observations are paired. An analysis of within-unit differences is generally more appropriate than treating the two sets as independent. Pairing can reduce the impact of baseline variation.

Independent-group comparisons apply when observations in one group do not correspond naturally to observations in the other. For means, t-based procedures are common, with a version that does not assume equal variances often being safer. For proportions, two-proportion methods or regression models may be appropriate. Categorical quality outcomes may be examined with chi-square methods, while count or rate outcomes may require Poisson or negative-binomial models. The method should follow the measurement scale, sampling design, and process structure—not the analyst’s preferred software menu.

Errors, Power, and the Cost of Being Wrong

Every statistical decision carries risks. A Type I error occurs when a true null hypothesis is rejected. In quality practice, this may lead an organization to implement an expensive redesign when the apparent improvement was random variation. A Type II error occurs when a false null hypothesis is not rejected. This may cause the organization to overlook a real increase in defects or abandon a beneficial intervention.

The significance level α is the long-run probability of Type I error under the stated testing procedure, not the probability that a particular conclusion is wrong. The probability of avoiding a Type II error is power, written as 1 − β. Power increases with larger sample size, larger true effect, lower variability, and a higher significance level. It also depends on whether the test is one-sided or two-sided.

A power analysis conducted before data collection can determine a sample size capable of detecting an effect that matters operationally. The analyst must specify a meaningful effect, an estimate of variability or baseline rate, the desired power, and the significance level. Sample-size calculations are not a substitute for sound design. A large, biased sample remains biased; a powered study measuring the wrong outcome remains uninformative.

In quality management, error costs are asymmetric. A false alarm about a harmless variation may waste resources, while failure to detect a safety-critical defect may cause serious harm. Therefore, α should not be selected mechanically. Regulatory requirements, customer risk, process capability, cost of investigation, and reversibility of the decision should influence the design. For repeated monitoring, ordinary single-test thresholds may produce excessive false alarms. Control-chart methods, sequential procedures, or adjusted significance levels may be more suitable.

Effect Size and Practical Significance

Statistical significance answers a limited question: is the observed result difficult to reconcile with the null model? Managers also need to know whether the magnitude is important. Effect size expresses the size of a difference or association independently, or partly independently, of sample size.

For a difference in means, the raw mean difference is often the most useful effect measure because it retains operational units—for example, a reduction of 2.4 minutes in waiting time. A standardized mean difference, such as Cohen’s d, divides the difference by a standard deviation and is useful for comparison across measures, but it may be less intuitive for operational decisions. For proportions, absolute risk difference, relative risk, and odds ratio provide different perspectives. In quality settings, the absolute change in defect rate is often more actionable than a relative percentage reduction alone.

Practical significance requires a decision threshold. A service organization may regard a reduction of at least three minutes as worthwhile, while a clinical process may require a reduction in adverse events large enough to justify training and technology costs. Such a threshold is sometimes called a minimally important difference or practical significance criterion. Confidence intervals help determine whether the data are compatible with effects above or below that threshold.

Consider an intervention that reduces defects from 4.0% to 3.8%. With a very large sample, this may be statistically significant. Yet the saving may not cover implementation costs. Conversely, reducing defects from 10% to 7% may be operationally valuable even if a small pilot produces p = 0.08. The appropriate conclusion is not simply “significant” or “not significant”; it is an assessment of estimated benefit, uncertainty, cost, risk, and feasibility.

A Decision Framework for Evidence-Based Quality Action

A robust evidence-based decision can be organized into five linked questions:

1. What is the decision population and quality characteristic? Define the unit, process, time frame, outcome, and target.

2. How were the data generated? Examine sampling, measurement validity, missing data, dependence, and possible confounding.

3. What is the estimated effect and its uncertainty? Report point estimates and confidence intervals, not only p-values.

4. Is the effect practically important? Compare the plausible effect with customer requirements, specifications, costs, and risk thresholds.

5. What action is proportionate? Options may include immediate containment, process redesign, further data collection, pilot implementation, or continued monitoring.

This framework prevents statistical testing from becoming detached from managerial judgment. Statistical evidence is one component of a decision system that also includes process knowledge, engineering analysis, customer voice, regulatory obligations, and ethical considerations.

Illustrative Case: Reducing Medication-Dispensing Errors

Background

The following is an illustrative case designed for learning. A hospital pharmacy introduces barcode verification intended to reduce dispensing errors. The quality team compares error rates during a four-week baseline period with rates during a four-week implementation period. An error is defined in advance as a dispensing event involving the wrong medicine, strength, or patient.

Situation and Problem

During the baseline period, 42 errors occur in 18,000 dispensing events. During implementation, 25 errors occur in 17,500 events. The observed rates are therefore approximately 0.233% and 0.143%, an absolute reduction of about 0.090 percentage points, or approximately 9 fewer errors per 10,000 dispensing events.

The pharmacy director asks whether the technology should be adopted permanently across all units. The quality analyst cautions that the periods differ in staffing, workload, and case mix. Moreover, the data are counts of relatively rare events, so the uncertainty around the difference may be substantial.

Analysis

The null hypothesis is that the error rate is unchanged; the alternative is that the implementation reduces the rate. The observed direction favours the intervention, but a rate comparison must account for the number of dispensing events in each period. A two-proportion or appropriate count-model analysis can estimate the difference and its confidence interval. The analyst should also examine whether the same units operated in both periods, whether reporting practices changed, and whether implementation was complete.

Suppose the analysis produces an estimated reduction of 0.090 percentage points with a 95% confidence interval from approximately 0.005 to 0.175 percentage points, together with a p-value slightly below 0.05. The result is statistically compatible with a reduction, but the interval shows that the true improvement could be small or considerably larger. The relative reduction may appear substantial, yet the absolute rate remains low; both descriptions are needed.

The team then examines operational consequences. Barcode verification requires equipment, staff training, maintenance, and contingency procedures when scanners fail. The potential benefit is not limited to the average number of errors prevented: the severity of a prevented error may be high. The team also finds that two wards used the technology inconsistently, and those wards had different case mixes.

Approach and Decision

Rather than treating the p-value as an automatic adoption rule, the hospital uses a staged decision. It continues the intervention in the wards where implementation is reliable, standardizes training, and collects several additional months of data. It stratifies results by ward and error type, monitors near misses, and checks whether reporting has changed. A cost and risk assessment is conducted alongside the statistical analysis.

The evidence supports continued use and further evaluation, but the original comparison alone does not establish that every observed improvement was caused by the technology. A controlled rollout or interrupted time-series analysis would strengthen causal inference. If ethical and operational conditions permit, phased implementation can provide comparison information while extending the safety intervention.

Outcome and Learning Points

The case illustrates several principles. Rare-event data require careful uncertainty assessment. Relative improvements can sound impressive while absolute changes remain small. Statistical significance does not settle questions of cost, severity, implementation fidelity, or generalizability. Finally, evidence-based quality decisions are iterative: measurement, analysis, action, and reassessment form a learning cycle rather than a one-time statistical verdict.

Common Misinterpretations and Analytical Risks

Several errors recur in organizational quality studies. The first is confusing correlation with causation. A lower defect rate after a new procedure may reflect the procedure, seasonal demand, staff changes, selective reporting, or regression to the mean. A stronger design and explicit consideration of alternative explanations are required.

The second is equating p > 0.05 with no effect. A non-significant result may indicate a genuinely negligible effect, inadequate sample size, excessive variability, poor measurement, or a wide confidence interval. Analysts should ask what effect sizes remain plausible.

The third is equating p < 0.05 with importance. Statistical significance can be produced by a trivial effect in a very large sample. Conversely, a result that is operationally important may deserve action while additional evidence is gathered, especially when the intervention is low-cost and reversible.

The fourth is conducting many unplanned tests and reporting only favourable results. Testing many outcomes, subgroups, or time periods increases the chance of at least one apparently significant finding. Pre-specification, transparent reporting, multiplicity adjustments where appropriate, and replication reduce this risk.

Other common problems include stopping data collection when significance is first reached, excluding inconvenient observations without a documented rule, ignoring missing data, using inappropriate averages for skewed data, and treating repeated measurements from the same unit as independent. Data visualization, process knowledge, sensitivity analysis, and consultation with subject-matter experts are valuable safeguards.

Governance, Ethics, and Digital Applications

Inferential results may affect employees, suppliers, patients, customers, and communities. Analysts must protect confidentiality, document definitions, preserve an audit trail, and report unfavorable findings as well as favourable ones. Quality metrics should not create incentives to suppress reporting or reclassify defects. When automated systems generate alerts or risk scores, responsible governance requires validation, monitoring for drift, explainability appropriate to the decision, and human review of consequential actions.

Modern quality platforms can automate sampling dashboards, interval estimates, hypothesis-test calculations, and power analyses. Automation improves consistency but does not determine whether a sample is representative or whether an effect is meaningful. Artificial intelligence and machine-learning systems may identify patterns in high-dimensional process data, but predictive accuracy does not automatically establish causal impact. A model that predicts defects may support targeted inspection; it does not by itself prove which intervention will reduce defects.

Current practice increasingly emphasizes estimation, reproducibility, preregistration of important analyses, transparent code, and integration of statistical evidence with process-monitoring systems. Bayesian methods are also used in some organizations to combine prior process knowledge with new data and to update the probability of competing explanations. These approaches are not substitutes for critical thinking; they provide additional ways to express uncertainty and support sequential learning.

Best Practices for Quality Analysts and Managers

A defensible inferential study normally follows these practices:

• Define the population, unit of analysis, outcome, comparison, and decision threshold before examining results.
• Use a sampling method appropriate to the process and document exclusions and missing data.
• Check measurement-system adequacy before interpreting small differences.
• Match the statistical method to the outcome type, study design, dependence structure, and distribution.
• Report effect estimates, confidence intervals, sample sizes, and p-values together when hypothesis testing is relevant.
• Distinguish statistical significance from practical significance and relate both to cost, risk, and customer requirements.
• Conduct power or precision planning before data collection.
• Investigate alternative explanations, confounding, regression to the mean, and changes in reporting.
• Avoid selective reporting, repeated unplanned testing, and post hoc changes to hypotheses.
• Translate findings into a proportionate action and specify how the result will be monitored after implementation.

Chapter Summary

Statistical inference enables quality professionals to use sample data to learn about broader processes while explicitly recognizing uncertainty. Sampling design determines whether generalization is credible, and the standard error describes the variability of a statistic across repeated samples. Confidence intervals communicate both an estimate and its precision. Hypothesis tests provide a structured comparison between a null model and an alternative, but a p-value is neither the probability that the null hypothesis is true nor a measure of practical importance.

Type I and Type II errors represent different risks, while power expresses the ability to detect an effect of a specified size. Effect sizes and confidence intervals are essential for judging whether a result matters operationally. Sound quality decisions combine statistical evidence with process knowledge, measurement validity, customer and regulatory requirements, cost, and risk. The most reliable practice is transparent, appropriately designed, and iterative: define the question, collect credible data, estimate the effect, assess uncertainty and practical significance, act proportionately, and continue learning.

Key Terms

Population: The complete set of units or conditions to which a study conclusion is intended to apply.

Sample: A subset of a population selected for observation or analysis.

Parameter: A numerical characteristic of a population, usually unknown.

Statistic: A numerical characteristic calculated from sample data.

Sampling distribution: The distribution of a statistic across repeated samples from a population.

Standard error: The standard deviation of a sampling distribution, representing sampling variability.

Confidence interval: An interval produced by a specified method to express uncertainty about a population parameter.

Null hypothesis: A reference claim, commonly representing no difference or no change.

Alternative hypothesis: A claim representing the effect or departure from the null hypothesis under investigation.

P-value: The probability, assuming the null model, of observing a result at least as extreme as the one obtained.

Significance level: The pre-specified threshold for rejecting the null hypothesis, denoted α.

Type I error: Rejection of a true null hypothesis.

Type II error: Failure to reject a false null hypothesis.

Statistical power: The probability of detecting a specified effect when that effect truly exists.

Effect size: A quantitative measure of the magnitude of a difference, relationship, or intervention impact.

Practical significance: The extent to which an effect is large enough to matter operationally or managerially.

Sampling bias: Systematic distortion caused by a sample that does not represent the target population.

Confounding: A situation in which another factor is associated with both the explanatory condition and the outcome, obscuring causal interpretation.

Regression to the mean: The tendency for unusually high or low observations to be followed by observations closer to the average.

Statistical significance: A result judged inconsistent with the null model at a specified significance level.

Review Questions

Short Answer Questions

1. Distinguish a population parameter from a sample statistic using a quality example.

2. What information does a confidence interval provide that a point estimate does not?

3. Explain why a p-value is not the probability that the null hypothesis is true.

4. Define Type I error, Type II error, and statistical power.

5. Why can a statistically significant result lack practical significance?

Long Answer Questions

1. Explain how sampling design, dependence, and measurement quality affect the validity of statistical inference in a TQM setting.

2. Describe the relationship among effect size, confidence interval, p-value, sample size, and practical significance.

3. Compare the consequences of Type I and Type II errors in a safety-critical quality process.

4. Explain how a quality analyst should design and report a before-and-after process-improvement study.

5. Discuss the limitations of using a p-value as the primary basis for managerial decision-making.

Analytical / Application Questions

1. A call centre reports a reduction in average waiting time from 16.0 to 14.5 minutes after training, with a 95% confidence interval for the reduction of 0.2 to 2.8 minutes. Interpret the result statistically and operationally.

2. A large production database finds a statistically significant defect reduction of 0.05 percentage points after a costly software upgrade. What additional evidence should managers examine before approving the upgrade across all plants?

3. A pilot study finds an important reduction in hospital errors but p = 0.08. Explain how power, confidence intervals, risk, cost, and study design should influence the next decision.

22. Multiple Choice Questions with Answers

Question 1

Which statement best describes a 95% confidence interval?

A. There is a 95% probability that the fixed parameter lies in the calculated interval.

B. Under repeated use of the same method, approximately 95% of such intervals would contain the parameter.

C. The sample mean will fall inside the interval 95% of the time.

D. The null hypothesis is true with 95% probability.

Correct Answer: B. Under repeated use of the same method, approximately 95% of such intervals would contain the parameter.

Question 2

A study reports p = 0.03 for a difference in defect rates. What is the most accurate interpretation?

A. There is a 3% probability that the null hypothesis is true.

B. There is a 97% probability that the intervention caused the improvement.

C. Assuming the null model, a result at least this extreme has probability 0.03.

D. The intervention has a practically important effect.

Correct Answer: C. Assuming the null model, a result at least this extreme has probability 0.03.

Question 3

Which change generally increases statistical power, all else being equal?

A. Reducing the sample size

B. Increasing measurement variability

C. Reducing the true effect size

D. Increasing the sample size

Correct Answer: D. Increasing the sample size

Question 4

A quality team fails to reject the null hypothesis in a small study. Which conclusion is most defensible?

A. The two processes are proven identical.

B. The intervention definitely has no effect.

C. The evidence is insufficient to reject the null under the specified method.

D. A Type I error has occurred.

Correct Answer: C. The evidence is insufficient to reject the null under the specified method.

Question 5

Which measure is usually most directly interpretable for an operational decision about defect reduction?

A. Absolute difference in defect rates

B. P-value alone

C. Sample size alone

D. Significance level alone

Correct Answer: A. Absolute difference in defect rates

Question 6

A team tests 30 outcomes and reports only the one with p < 0.05. What is the principal risk?

A. Reduced statistical power caused by a larger sample

B. Inflated false-positive risk from multiple testing

C. Guaranteed Type II error

D. Removal of all sampling bias

Correct Answer: B. Inflated false-positive risk from multiple testing

Question 7

Which situation most clearly calls for a paired analysis?

A. Comparing randomly selected customers from two unrelated regions

B. Comparing two independent suppliers using different products

C. Measuring the same machines before and after maintenance

D. Comparing defects from two unrelated factories

Correct Answer: C. Measuring the same machines before and after maintenance

Question 8

A very large sample produces a statistically significant reduction of 0.01 minutes in cycle time. What should the manager do first?

A. Assume the improvement is strategically important.

B. Ignore the result because all significant findings are misleading.

C. Assess the effect size against operational thresholds and implementation cost.

D. Conclude that the sample must be biased.

Correct Answer: C. Assess the effect size against operational thresholds and implementation cost.

Question 9

Which is an example of a Type I error in quality management?

A. Failing to detect a real increase in defects

B. Rejecting no-change when the process has not actually changed

C. Using a sample rather than a census

D. Obtaining a wide confidence interval

Correct Answer: B. Rejecting no-change when the process has not actually changed

Question 10

Why can a narrow confidence interval still support a misleading conclusion?

A. Precision does not remove systematic sampling or measurement bias.

B. Narrow intervals always indicate Type II error.

C. Confidence intervals cannot be used with quality data.

D. A narrow interval proves practical significance.

Correct Answer: A. Precision does not remove systematic sampling or measurement bias.