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
L = ?Up̂ = 275/500E99%

In a poll of 500 randomly chosen voters, 275 support a proposal. Find the lower limit of the 99% confidence interval for the proportion of supporters.

n = 500x = 27599%
lower limit =
2.Easy
n = 40, σ = 8LUx̄ = 74.5E = ?95%

A sample of 40 measurements has mean 74.5. The population standard deviation is known to be 8. Find the margin of error E of a 95% confidence interval for the mean.

n = 40x̄ = 74.5σ = 895%
E =
3.Medium
n = 30, s = 13.5L = ?Ux̄ = 117E95%

A sample of 30 items has mean 117 and standard deviation s = 13.5. The population is roughly normal. Find the lower limit of the 95% confidence interval for the mean.

n = 30x̄ = 117s = 13.595%t(29) = 2.045
lower limit =
4.Medium
n = 6, s = 10.5LU = ?x̄ = 80E99%

A sample of 6 items has mean 80 and standard deviation s = 10.5. The population is roughly normal. Find the upper limit of the 99% confidence interval for the mean.

n = 6x̄ = 80s = 10.599%t(5) = 4.032
upper limit =
5.Hard
σ = 36, n = ?x̄ − Ex̄ + Ex̄E = 290%

The population standard deviation is 36. 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 = 36E = 290%
n =
6.Hard
σ = 37, n = ?x̄ − Ex̄ + Ex̄E = 0.595%

The population standard deviation is 37. 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 0.5?

σ = 37E = 0.595%
n =

Answer key

  1. 1. lower limit = 0.4927
  2. 2. E = 2.479
  3. 3. lower limit = 112
  4. 4. upper limit = 97.28
  5. 5. n = 877
  6. 6. n = 21037

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