# Intervals, tests and uncertainty

> A value computed from sample data to approximate a population quantity.

Course: [Practical statistics and inference](https://studybrix.com/en/courses/statistics-foundations/index.md)
Level: university
Prerequisites: High-school algebra.

## Notes

### Estimate

A value computed from sample data to approximate a population quantity.

### Confidence interval

A range produced by a method designed to capture a population parameter at a stated long-run rate under assumptions.

### Null hypothesis

A specified reference claim used in a significance test.

### P-value

A probability, under the null model, of data at least as incompatible with that model as the observed result by the test statistic.

## Practice questions

### 1. Which term best matches this description: A value computed from sample data to approximate a population quantity.

A. Estimate
B. Null hypothesis
C. Confidence interval
D. P-value

Answer: Estimate

Explanation: Estimate is the matching concept in this lesson.

### 2. Which term best matches this description: A range produced by a method designed to capture a population parameter at a stated long-run rate under assumptions.

A. Estimate
B. P-value
C. Null hypothesis
D. Confidence interval

Answer: Confidence interval

Explanation: Confidence interval is the matching concept in this lesson.

### 3. Which concept would you apply first in a situation where a specified reference claim used in a significance test.

A. Estimate
B. P-value
C. Confidence interval
D. Null hypothesis

Answer: Null hypothesis

Explanation: The scenario directly calls for Null hypothesis.

### 4. Name the concept described as: A probability, under the null model, of data at least as incompatible with that model as the observed result by the test statistic.

Answer: P-value

Explanation: The intended concept is P-value.

### 5. Which statement about Estimate is most accurate?

A. A probability, under the null model, of data at least as incompatible with that model as the observed result by the test statistic.
B. A value computed from sample data to approximate a population quantity.
C. A range produced by a method designed to capture a population parameter at a stated long-run rate under assumptions.
D. A specified reference claim used in a significance test.

Answer: A value computed from sample data to approximate a population quantity.

Explanation: The definition in the lesson notes gives the required condition.

### 6. Explain one important difference between Estimate and Confidence interval.

Sample answer / marking guidance: Estimate: A value computed from sample data to approximate a population quantity. Confidence interval: A range produced by a method designed to capture a population parameter at a stated long-run rate under assumptions.

Explanation: Credit a clear distinction using both definitions and an appropriate example if supplied.

### 7. Give a short example showing how Null hypothesis would be used in practice.

Sample answer / marking guidance: A valid example should demonstrate this idea: A specified reference claim used in a significance test.

Explanation: Credit a relevant scenario that applies the concept rather than merely naming it.

### 8. Summarize why P-value matters in the lesson “Intervals, tests and uncertainty”.

Sample answer / marking guidance: P-value matters because A probability, under the null model, of data at least as incompatible with that model as the observed result by the test statistic.

Explanation: Credit the core purpose, scope and any important limitation from the notes.

## Further reading

- https://www.openintro.org/book/os/

Original AI-assisted educational draft; not independently teacher-reviewed. References support further study, not copied exercises, affiliation or curriculum accreditation.