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
LUW = ?

A laboratory measures a quantity 50 times; the measurement standard deviation is known to be 8. How wide W is the 99% confidence interval for the true mean (upper limit minus lower limit)?

n = 50σ = 899%
W =
2.Easy
n = 80, σ = 29LU = ?x̄ = 150.5E95%

A sample of 80 measurements has mean 150.5. The population standard deviation is known to be 29. Find the upper limit of the 95% confidence interval for the mean.

n = 80x̄ = 150.5σ = 2995%
upper limit =
3.Medium
n = 16, s = 11LU = ?x̄ = 92E90%

A sample of 16 items has mean 92 and standard deviation s = 11. The population is roughly normal. Find the upper limit of the 90% confidence interval for the mean.

n = 16x̄ = 92s = 1190%t(15) = 1.753
upper limit =
4.Medium
n = 9, s = 17LUx̄ = 16.5E = ?99%

A sample of 9 items has mean 16.5 and standard deviation s = 17. The population is roughly normal. Find the margin of error E of a 99% confidence interval for the mean.

n = 9x̄ = 16.5s = 1799%t(8) = 3.355
E =
5.Hard
σ = 13, n = ?x̄ − Ex̄ + Ex̄E = 295%

The population standard deviation is 13. 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?

σ = 13E = 295%
n =
6.Hard
p ≈ 0.7, n = ?p̂ − Ep̂ + Ep̂E = 0.0190%

A pilot study suggests that about 0.7 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 0.01?

p ≈ 0.7E = 0.0190%
n =

Answer key

  1. 1. W = 5.829
  2. 2. upper limit = 156.9
  3. 3. upper limit = 96.82
  4. 4. E = 19.01
  5. 5. n = 163
  6. 6. n = 5683

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