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 = 49, σ = 6LU = ?x̄ = 96.5E95%

A sample of 49 measurements has mean 96.5. The population standard deviation is known to be 6. Find the upper limit of the 95% confidence interval for the mean.

n = 49x̄ = 96.5σ = 695%
upper limit =
2.Easy
110.85x̄115.1599%

A 99% confidence interval for a mean, computed from 36 observations with a known population standard deviation, is [110.85, 115.15]. What standard deviation σ was used?

[110.85, 115.15]n = 3699%
σ =
3.Medium
μ₁ − μ₂0LU = ?x̄₁ − x̄₂E90%

The battery life of two phone models is compared. Model 1: 100 phones, mean 123 h, known standard deviation 8 h. Model 2: 40 phones, mean 116.5 h, known standard deviation 11 h. Find the upper limit of the 90% confidence interval for μ₁ − μ₂.

n₁ = 100x̄₁ = 123 hσ₁ = 8 hn₂ = 40x̄₂ = 116.5 hσ₂ = 11 h90%
upper limit = h
4.Medium
n = 20, s = 3LUx̄ = 57.5E = ?95%

A sample of 20 items has mean 57.5 and standard deviation s = 3. The population is roughly normal. Find the margin of error E of a 95% confidence interval for the mean.

n = 20x̄ = 57.5s = 395%t(19) = 2.093
E =
5.Hard
σ = 21, n = ?x̄ − Ex̄ + Ex̄E = 1.590%

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 1.5?

σ = 21E = 1.590%
n =
6.Hard
σ = 28, n = ?x̄ − Ex̄ + Ex̄E = 2.595%

The population standard deviation is 28. 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 = 28E = 2.595%
n =

Answer key

  1. 1. upper limit = 98.18
  2. 2. σ = 5.008
  3. 3. upper limit = 9.649 h
  4. 4. E = 1.404
  5. 5. n = 531
  6. 6. n = 482

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