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 = 400/1000E90%

In a poll of 1000 randomly chosen voters, 400 support a proposal. Find the lower limit of the 90% confidence interval for the proportion of supporters.

n = 1000x = 40090%
lower limit =
2.Easy
n = 49, σ = 2LU = ?x̄ = 113.5E99%

A sample of 49 measurements has mean 113.5. The population standard deviation is known to be 2. Find the upper limit of the 99% confidence interval for the mean.

n = 49x̄ = 113.5σ = 299%
upper limit =
3.Medium
n = 16, s = 18.5L = ?Ux̄ = 66E90%

A sample of 16 items has mean 66 and standard deviation s = 18.5. The population is roughly normal. Find the lower limit of the 90% confidence interval for the mean.

n = 16x̄ = 66s = 18.590%t(15) = 1.753
lower limit =
4.Medium
n = 21, s = 4LU = ?x̄ = 114E90%

A sample of 21 items has mean 114 and standard deviation s = 4. The population is roughly normal. Find the upper limit of the 90% confidence interval for the mean.

n = 21x̄ = 114s = 490%t(20) = 1.725
upper limit =
5.Hard
σ = 40, n = ?x̄ − Ex̄ + Ex̄E = 599%

The population standard deviation is 40. 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 5?

σ = 40E = 599%
n =
6.Hard
p ≈ 0.3, n = ?p̂ − Ep̂ + Ep̂E = 0.0590%

A pilot study suggests that about 0.3 of products are defective. How many products n must be inspected so that a 90% confidence interval for the proportion has a margin of error of at most 0.05?

p ≈ 0.3E = 0.0590%
n =

Answer key

  1. 1. lower limit = 0.3745
  2. 2. upper limit = 114.2
  3. 3. lower limit = 57.89
  4. 4. upper limit = 115.5
  5. 5. n = 425
  6. 6. n = 228

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