Practice Confidence Interval in Math

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

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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.

Showing a random 20 of 50 problems.

Example 1

hard
Find the smallest n for a 95% CI for a proportion with E≤0.03, assuming worst case p^=0.5, z∗=1.96.

Example 2

medium
A 95% CI for the mean is (95.1,104.9). A colleague claims 'there is a 95% probability the true mean lies in this interval.' What is the correct interpretation?

Example 3

easy
A 95% CI for a mean is (46,54). What is the point estimate (the center)?

Example 4

medium
A 95% CI for the difference in means is (−2,6). Does this suggest a significant difference at α=0.05?

Example 5

medium
To halve the width of a 95% CI for a mean (same σ, same confidence), by what factor must n increase?

Example 6

medium
A 99% CI (z∗=2.576) uses xˉ=60, σ=10, n=25. Find the interval.

Example 7

hard
A 98% CI for μ with xˉ=50, σ=20, n=100, z∗=2.326. Find the CI.

Example 8

easy
Should you use a z-interval or a t-interval when σ is unknown and n is small?

Example 9

medium
Compute a 95% CI for μ given xˉ=50, σ=10, n=100, z∗=1.96.

Example 10

easy
True or false: increasing the sample size n (same confidence) narrows the interval.

Example 11

hard
If 100 different 95% CIs are constructed from independent samples, about how many are expected to miss the true mean?

Example 12

easy
A 95% CI for μ is (8,12). What is the width of the interval?

Example 13

hard
A 95% CI for a proportion: p^=0.32, n=400, z∗=1.96. Find the CI.

Example 14

medium
A 95% CI for the difference of means is (1.2,4.8). Is the difference significantly different from zero?

Example 15

easy
A 95% CI for μ is (20,30). State the point estimate and the margin of error.

Example 16

medium
A 95% CI is (10,14). What is the E, and what was xˉ?

Example 17

easy
True or false: increasing the confidence level from 90% to 99% (same data) makes the interval wider.

Example 18

medium
For a proportion with p^=0.6, n=100, build a 95% CI (z∗=1.96).

Example 19

easy
A sample gives point estimate xˉ=50 with margin of error 4. Write the 95% confidence interval.

Example 20

easy
What z∗ value corresponds to a 90% confidence level?
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