Statistics Final Exam
A free Statistics and Data Analysis lesson from the “Inference and Conclusions” unit, with a worked example and practice problems including step-by-step solutions.
This untimed final has 44 independent questions from all five course units, with extra weight on inference. Use a calculator where appropriate and show your work separately. Review each answer's reasoning after submission. For a fuller demonstration of statistical practice, complete the optional written investigation separately and have a teacher or tutor assess its assumptions, calculations and contextual conclusions with the rubric.
What you'll learn
- Apply data analysis, study design, probability and inference across all five units
- Select procedures, check their conditions and calculate required summaries or statistics
- Interpret results in context and distinguish association, causation and generalization
Worked example
Problem. Which variable is categorical?
- Categorical variables name groups or labels.
- Favorite app is a label rather than a measurement.
Answer: Favorite app
Lesson preview: this page shows 5 practice items. The interactive activity contains 30 practice items and 44 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. Review case A: Which variable is categorical?
Choices: Minutes studied · Number of siblings · Favorite app · Height in inches
Show solution
- Categorical variables name groups or labels.
- Favorite app is a label rather than a measurement.
Answer: Favorite app
2. Review case B: Which variable is quantitative?
Choices: Device brand · Time in minutes · Eye color · Lunch choice
Show solution
- Quantitative variables measure amounts.
- Time in minutes is numerical and can be averaged.
Answer: Time in minutes
3. Review case C: A frequency table shows 8 first-choice votes, 12 second-choice votes, and 6 third-choice votes. How many responses are in the table?
Show solution
- Add all category counts: 8 + 12 + 6.
- The total is 26.
Answer: 26
4. Review case D: A box plot has Q1 = 9, median = 11, and Q3 = 13. Find the IQR.
Show solution
- IQR measures the spread of the middle half.
- 13 - 9 = 4.
Answer: 4
5. Review case E: Find the median of 17, 8, 20, 11, 14.
Show solution
- Order the data from least to greatest.
- The middle value is 14.
Answer: 14
Explain and apply
Complete these tasks on paper. Use the rubric to review your reasoning with a teacher or study partner; these tasks are not automatically scored.
Complete a two-proportion investigation
Independent simple random samples of 100 households from each of two large cities find that 64 in City A and 48 in City B compost. Test H0: pA=pB against Ha: pA!=pB at alpha=.05, then construct a 95% interval for pA−pB. Use z*=1.96 and the supplied two-sided test p-value .0227. Define the parameter, justify the two standard errors, check conditions, and interpret both conclusions in context.
Review rubric and solution
- Define pA and pB as the cities' household composting proportions, preserving A-minus-B order.
- Check independent random samples, sampling fractions no greater than 10%, and large observed and null-expected counts.
- Pool for the equality test: p-pooled=.56; SE0=√(.56×.44×.02)≈.07020; z≈2.279.
- Since .0227<.05, reject equal proportions and state evidence of a population difference.
- For the interval use unpooled SE=√(.64×.36/100+.48×.52/100)≈.06928; interval=.16±.13579≈(.0242,.2958).
- Interpret an estimated 2.4 to 29.6 percentage-point advantage for A; do not infer that city residence causes composting.
- The null-model pooled estimate is 112/200=.56. The test statistic is .16/√(.56×.44×.02)≈2.279, with the supplied two-sided p-value about .0227.
- The interval uses the separate estimates: .16±1.96√(.64×.36/100+.48×.52/100)≈(.0242,.2958).
- Both analyses support a higher composting proportion in City A at these levels, under the sampling and approximation assumptions. The observational comparison does not establish a causal city effect.
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