Practice workbook

Attempt these 36 exercises before opening the separate solutions. Show the denominator, units and reasoning, even if you use software. Each lesson has three tasks: a calculation, an explanation and a transfer or critique. A calculator is enough for the small examples. Use the dictionary and supplied CSVs for file-based tasks.

Lesson 1

1A Define the unit

A delivery table has 100 unique shipment IDs. After joining tracking events it has 340 rows. Write a question the 340-row count answers and a question requiring 100 as the denominator. Explain why treating 340 rows as 340 independent shipments is wrong.

1B Keep unknowns visible

Six shipments have known late statuses: 1, 0, 0, 1, 0, 1. Two more have unknown timing. Calculate the observed late fraction among evaluable shipments. Write a one-sentence result including coverage. Give the possible all-eight late-rate bounds without assuming the missing statuses.

1C Write an analysis contract

For “Which service is more reliable?”, define population, period, unit, outcome, comparator and one limitation using the main shipment fixture. Explain why a comparison of actual minutes alone may not answer your question.

Lesson 2

2A Change the tail

For 8, 9, 10, 11, 12, 60 minutes, calculate mean, median, linear Q1, Q3 and IQR. Compare with the lesson's original six values. Which summaries changed?

2B Investigate a flag

An analyst deletes every duration beyond a 1.5-IQR fence and reports the reduced mean as “the true average.” Identify two problems and propose a transparent analysis policy.

2C Interpret ratings

Two groups each have mean rating 3. Group A's ratings are 3, 3, 3, 3; B's are 1, 1, 5, 5. Explain what the mean hides and choose a useful display.

Lesson 3

3A Match the question

Choose a chart for each: distribution of 240 delivery durations; late rate by service; late rate over eight ordered weeks; relationship between distance and duration. State axes and units.

3B Repair the display

A bar chart compares rates of 48% and 52% with an axis from 47% to 53%, no denominators and the title “Performance doubled.” Describe the corrected display and a defensible title.

3C Write a text alternative

Write two sentences describing Lesson 3’s illustrative hub chart for a reader who cannot see it: East has 18/120 late shipments and West has 12/120. Include rates, direction, absolute percentage-point gap, denominators and the observational limitation. These are the lesson’s toy values, not the main fixture.

Lesson 4

4A Sampling versus assignment

A company recruits 40 volunteers from one shift and randomly assigns 20 to a checklist. Which feature supports a causal comparison within the study? Which limitation affects generalization? Name a condition under which even the within-study comparison could be compromised.

4B Bound missing ratings

Eight of ten ratings are observed with sum 32; the scale is 1–5. Calculate the respondent mean and the lowest/highest possible all-ten mean. Are these bounds a confidence interval?

4C Count independent units

A trial records ten tasks from each of four people. Explain why this is different from one task each from 40 people. What design or method information would you request before computing a standard error?

Lesson 5

5A Change the base rate

Among 1,000 hypothetical jobs, 200 are delayed. An alert catches 80% of delayed jobs and flags 10% of non-delayed jobs. Complete the four-cell table and calculate the fraction of alerts that identify delayed jobs.

5B Use a complement

Under a separate independent-trial model with late probability 0.10 per delivery, calculate the probability that at least one of three deliveries is late. State the assumption needed to multiply probabilities.

5C Read the condition

Using the lesson's priority example, explain the difference between P(late given priority), P(priority given late) and P(priority and late). Give the three fractions.

Lesson 6

6A Change sample size

A sample SD is 6 minutes. Calculate the estimated SE for n=9 and n=36 independent observations, assuming SD remains 6. Explain why the individual SD did not halve.

6B Read the miniature sampling table

From the nine equally likely ordered samples in Lesson 6, calculate the probability that the sample mean equals 4 and the probability it is at least 5. Is either probability the chance that the population mean equals 4?

6C Identify false precision

A report says “We repeated each of 12 measurements ten times, so our 120-row dataset has the precision of 120 independent participants.” Identify the missing assumption and explain why additional rows may contribute less information than claimed.

Lesson 7

7A Build an interval

For an independent normal sample with n=16, mean=20 minutes and sample SD=4, use t*=2.131 to calculate a two-sided 95% mean-confidence interval. Show SE and margin.

7B Repair the interpretation

Rewrite: “There is a 95% probability that the fixed population mean lies in this calculated interval, and 95% of people finish inside it.” Distinguish the two errors.

7C Change the confidence level

For unchanged data, would a 99% interval be wider or narrower than a 95% interval? Explain the trade-off and name one uncertainty that neither automatically covers.

Lesson 8

8A Explain the trial

Use the actual trial results to write three sentences: effect and direction; interval and p-value; one model/design limitation. Do not use “proves,” “chance the null is true,” or an individual guarantee.

8B Read a non-rejection

A different trial estimates checklist−control at −1 minute with a 95% interval from −6 to +4 and p=0.68. Can you conclude equivalence or no effect? Explain a plausible benefit and harm compatible with the interval.

8C Match study to method

For each scenario, identify why the independent-groups Welch method is appropriate or incomplete: different people assigned to two groups; the same people before and after; 40 tasks performed by four randomized teams. No new method formulas are required.

Lesson 9

9A Report both scales

A late rate changes from 12% to 9%. Calculate absolute percentage-point change and relative percentage change. Explain why “down 3%” is ambiguous.

9B Standardize a mixture

Use the Lesson 9 on-time table. Calculate each hub's rate for a target population containing 80% short and 20% long routes. Compare with the equal-mixture results and explain why changing weights changes the question.

9C Apply a practical threshold

The actual trial interval is −5.85 to −0.55 minutes. A worthwhile reduction is at least 2 minutes. Explain whether the interval excludes no improvement, whether it establishes the worthwhile threshold, and what decision you recommend given the data is simulated.

Lesson 10

10A Calculate and interpret

Use fitted minutes=12.6622+1.8058×km. Calculate the fitted value at 40 km. For a hypothetical observed duration of 90 minutes, calculate the residual. Interpret its sign.

10B Critique a claim

A slide says “r=0.923 proves distance causes 92.3% of delays.” Identify at least three problems with that sentence. Rewrite it accurately.

10C Check the support

The recorded distances range from 5.2 to 54.8 km. Explain why the intercept at zero and a prediction at 100 km require caution. Name two patterns you would look for in a residual plot.

Lesson 11

11A Write for a decision

Write a 100–150-word brief recommending an operational investigation using the shipment results. Include scope, a checked finding, a confounding or missingness limitation and a next step. Do not assign causal blame.

11B Separate the roles

Label each as observation, interpretation or recommendation: “20 of 51 late shipments have missing ratings”; “Respondent ratings may overstate all-shipment satisfaction”; “Investigate response barriers before claiming overall satisfaction improved.” Explain the inference connecting them.

11C Challenge an AI summary

An AI-generated draft says: “West is clearly superior, the checklist proves a 13% productivity gain, and the 4.14 average rating represents everyone.” Identify evidence needed for each claim and rewrite the three sentences with appropriate limits.

Lesson 12

12A Pre-specify a plan

Draft the capstone analysis contract before consulting the reference answer. Identify one primary trial contrast and one exploratory shipment question. State what you will retain in an audit trail if the plan changes.

12B Trace a number

Choose one chart label from your capstone. Trace it to source file, column definitions, inclusion policy, calculation and rounding. Ask another learner to reproduce it without your help.

12C Transfer the reasoning

If tomorrow's evidence came from 40 observations on four people rather than 40 independent people, write a short note explaining which inferential claims need revision and why your descriptive arithmetic may still be correct.