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
n = 50, σ = 10L = ?Ux̄ = 24.5E95%

A sample of 50 measurements has mean 24.5. The population standard deviation is known to be 10. Find the lower limit of the 95% confidence interval for the mean.

n = 50x̄ = 24.5σ = 1095%
lower limit =
2.Easy
L = ?Up̂ = 143/250E95%

In a poll of 250 randomly chosen voters, 143 support a proposal. Find the lower limit of the 95% confidence interval for the proportion of supporters.

n = 250x = 14395%
lower limit =
3.Medium
n = 7, s = 18.5LUx̄ = 89E = ?95%

A sample of 7 items has mean 89 and standard deviation s = 18.5. The population is roughly normal. Find the margin of error E of a 95% confidence interval for the mean.

n = 7x̄ = 89s = 18.595%t(6) = 2.447
E =
4.Medium
n = 25, s = 4.5LUx̄ = 37.5E = ?90%

A sample of 25 items has mean 37.5 and standard deviation s = 4.5. The population is roughly normal. Find the margin of error E of a 90% confidence interval for the mean.

n = 25x̄ = 37.5s = 4.590%t(24) = 1.711
E =
5.Hard
σ = 38, n = ?x̄ − Ex̄ + Ex̄E = 299%

The population standard deviation is 38. 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 2?

σ = 38E = 299%
n =
6.Hard
n = 25σ = ?Us = 2.995%

The diameters of 25 machined shafts have a sample standard deviation of 2.9 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 = 2.9 µmχ² = 12.401, 39.364
σ = µm

Answer key

  1. 1. lower limit = 21.73
  2. 2. lower limit = 0.5107
  3. 3. E = 17.11
  4. 4. E = 1.54
  5. 5. n = 2396
  6. 6. σ = 2.264 µm

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