Practice Confidence Interval in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A range of values, computed from sample data, that is likely to contain the true population parameter with a specified level of confidence.

You can't know the exact average height of all Americans, but after measuring 200 people you can say: 'I'm 95\% confident the true average is between 167 cm and 173 cm.' It's like casting a net—wider nets catch the true value more often, but narrower nets are more useful. A 95\% confidence level means that if you repeated this process 100 times, about 95 of those nets would contain the true value.

Example 1

medium
A sample of n=64 has \bar{x}=85 and s=16. Construct a 95% confidence interval for the population mean.

Example 2

hard
Compare 90% and 99% confidence intervals for \bar{x}=100, s=15, n=36. Calculate both and explain the trade-off between confidence and precision.

Example 3

easy
A 95% CI for a population mean is (42, 58). Find the sample mean \bar{x} and the margin of error E.

Example 4

hard
To achieve a margin of error of E=3 with 95% confidence, given \sigma=20, find the required sample size n.
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