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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
41.72x̄47.2895%

A 95% confidence interval for a mean, computed from 144 observations with a known population standard deviation, is [41.72, 47.28]. What standard deviation σ was used?

[41.72, 47.28]n = 14495%
σ =
2.Easy
LUW = ?

A laboratory measures a quantity 36 times; the measurement standard deviation is known to be 12. How wide W is the 95% confidence interval for the true mean (upper limit minus lower limit)?

n = 36σ = 1295%
W =
3.Medium
x̄E₁ = 8.395%, n = 25x̄E₂ = ?99%, n = 25

A 95% confidence interval for a mean, based on 25 observations and a known σ, has a margin of error of 8.3. What is the margin of error E₂ of a 99% interval from the same data?

95%n₁ = 25E₁ = 8.399%
E₂ =
4.Medium
n = 10, s = 2L = ?Ux̄ = 66.5E99%

A sample of 10 items has mean 66.5 and standard deviation s = 2. The population is roughly normal. Find the lower limit of the 99% confidence interval for the mean.

n = 10x̄ = 66.5s = 299%t(9) = 3.25
lower limit =
5.Hard
n = 16Lσ = ?s = 5.995%

The diameters of 16 machined shafts have a sample standard deviation of 5.9 µm. Assuming the diameters are normally distributed, find the upper limit σ of the 95% confidence interval for the population standard deviation. With df = 15, 2.5% of the χ² distribution lies below 6.262 and 2.5% lies above 27.488.

n = 16s = 5.9 µmχ² = 6.262, 27.488
σ = µm
6.Hard
σ = 3, n = ?x̄ − Ex̄ + Ex̄E = 0.590%

The population standard deviation is 3. 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 0.5?

σ = 3E = 0.590%
n =

Answer key

  1. 1. σ = 17.02
  2. 2. W = 7.84
  3. 3. E₂ = 10.91
  4. 4. lower limit = 64.44
  5. 5. σ = 9.131 µm
  6. 6. n = 98

Full step-by-step solutions: practise this topic on examproblems.com.