Inference and Conclusions Checkpoint
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 checkpoint reviews sampling variability, confidence intervals, hypothesis tests, p-values, error types, chi-square reasoning, and statistical conclusions.
What you'll learn
- Review the major skills from this part of the course
- Choose an appropriate statistical method
- Explain results in context
Worked example
Problem. Two random samples from the same school give slightly different sample proportions. What idea explains the difference?
- Different random samples usually give different statistics.
- That sample-to-sample change is sampling variability.
Answer: sampling variability
Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Review case A: Which value is fixed but usually unknown?
Choices: the response option order · the true value for the whole population · the value from one sample · the treatment assignment
Show solution
- The parameter describes the population.
- A sample statistic estimates it.
Answer: the true value for the whole population
2. Review case B: Why do confidence intervals depend on standard error?
Choices: it removes the need for a sample · it tells whether a question is biased · it measures how much the statistic tends to vary · it proves causation
Show solution
- Inference depends on sampling variability.
- Standard error measures that variability.
Answer: it measures how much the statistic tends to vary
3. Review case C: Which interpretation overstates what an interval says?
Choices: the interval estimates the population proportion · the interval has uncertainty · the sample proportion is the center · the interval proves the exact population proportion
Show solution
- Intervals estimate; they do not prove exact values.
- Uncertainty remains.
Answer: the interval proves the exact population proportion
4. Review case D: Which conclusion overstates an interval estimate?
Choices: every individual value falls inside the interval · the population mean is plausibly in the interval · the interval has uncertainty · the center is the sample mean
Show solution
- A mean interval estimates an average.
- It does not claim all individual values are inside.
Answer: every individual value falls inside the interval
5. Review case E: In a hypothesis test, the null hypothesis usually represents:
Choices: the final proof of causation · the default claim being tested · the strongest possible conclusion · the sample size
Show solution
- The null is the starting claim.
- Evidence is measured against it.
Answer: the default claim being tested
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