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

In a poll of 200 randomly chosen voters, 96 support a proposal. Find the margin of error E of a 95% confidence interval for the proportion of supporters.

n = 200x = 9695%

E =

2.Easy

A sample of 144 measurements has mean 67.5. The population standard deviation is known to be 28. Find the margin of error E of a 95% confidence interval for the mean.

n = 144x̄ = 67.5σ = 2895%

E =

3.Medium

A sample of 6 items has mean 112 and standard deviation s = 4. The population is roughly normal. Find the margin of error E of a 99% confidence interval for the mean.

n = 6x̄ = 112s = 499%t(5) = 4.032

E =

4.Medium

A sample of 13 items has mean 34 and standard deviation s = 18. The population is roughly normal. Find the lower limit of the 99% confidence interval for the mean.

n = 13x̄ = 34s = 1899%t(12) = 3.055

lower limit =

5.Hard

The population standard deviation is 21. How large a sample n do you need so that a 90% confidence interval for the mean has a margin of error of at most 2?

σ = 21E = 290%

n =

6.Hard

The diameters of 25 machined shafts have a sample standard deviation of 6.8 µm. Assuming the diameters are normally distributed, find the lower limit σ of the 95% confidence interval for the population standard deviation. With df = 24, 2.5% of the χ² distribution lies below 12.401 and 2.5% lies above 39.364.

n = 25s = 6.8 µmχ² = 12.401, 39.364

σ = µm

Answer key

1. E = 0.06924
2. E = 4.573
3. E = 6.584
4. lower limit = 18.75
5. n = 299
6. σ = 5.31 µm

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