The confidence interval
The confidence interval of a mean and of a proportion: standard error, quantile, margin of error, bounds, what the confidence level means and the sample size that guarantees a given margin.
- 25 cards
- 6 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- Sort and link
- The numbers
- Scenarios
- Understand
A few cards from the deck
Confidence interval: what is it?
Show the answer
A range of values computed from the sample by a method that, from one sample to the next, brackets the unknown parameter with a probability chosen in advance.
It replaces a single value, necessarily wrong, with an honest range. General form: estimate ± margin of error.
100 measurements have a mean of 250 ms and a known standard deviation of 40 ms. What is the 95% confidence interval of the mean?
- [242.2; 257.8]
- [210; 290]
- [249.6; 250.4]
- [245.0; 255.0]
Show the answer
[242.2; 257.8]
Standard error: 40 / √100 = 4. Margin: 1.96 × 4 = 7.84. Bounds: 250 ± 7.84. [210; 290] forgets to divide by √n and describes the data, not the mean.
For a mean, the confidence interval is written: observed mean ± … × ….
Show the answer
For a mean, the confidence interval is written: observed mean ± quantile × standard error.
The quantile is 1.96 at 95% with the normal distribution. When the standard deviation is estimated from the sample, the Student quantile is used.
Confidence level: what is it?
Show the answer
The share of possible samples whose interval, built by the same method, contains the true value.
It describes the method, not a given interval. Once computed, the interval either contains the true value or does not: the value itself is fixed.