Confidence intervals worksheet with answers

Free printable Confidence intervals worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A sample of 200 measurements has mean 153. The population standard deviation is known to be 13. Find the upper limit of the 99% confidence interval for the mean.

n = 200x̄ = 153σ = 1399%

upper limit =

2.Easy

In a poll of 800 randomly chosen voters, 456 support a proposal. Find the margin of error E of a 95% confidence interval for the proportion of supporters.

n = 800x = 45695%

E =

3.Medium

A sample of 6 items has mean 95 and standard deviation s = 10.5. The population is roughly normal. Find the margin of error E of a 99% confidence interval for the mean.

n = 6x̄ = 95s = 10.599%t(5) = 4.032

E =

4.Medium

A 95% confidence interval for a mean, based on 100 observations and a known σ, has a margin of error of 1.9. What is the margin of error E₂ if the same study uses 25 observations instead?

95%n₁ = 100E₁ = 1.9n₂ = 25

E₂ =

5.Hard

The population standard deviation is 35. How large a sample n do you need so that a 95% confidence interval for the mean has a margin of error of at most 2.5?

σ = 35E = 2.595%

n =

6.Hard

The population standard deviation is 14. How large a sample n do you need so that a 99% confidence interval for the mean has a margin of error of at most 3?

σ = 14E = 399%

n =

Answer key

1. upper limit = 155.4
2. E = 0.03431
3. E = 17.28
4. E₂ = 3.8
5. n = 753
6. n = 145

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