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 40 times; the measurement standard deviation is known to be 17.5. How wide W is the 95% confidence interval for the true mean (upper limit minus lower limit)?

n = 40σ = 17.595%
W =
2.Easy
93.58x̄99.4290%

A 90% confidence interval for a mean, computed from 81 observations with a known population standard deviation, is [93.58, 99.42]. What standard deviation σ was used?

[93.58, 99.42]n = 8190%
σ =
3.Medium
n = 9, sd​ = 1.70LU = ?d̄ = 5.1E95%

The blood pressure of 9 patients is measured before and after a treatment. The differences d = before − after (mmHg) have mean 5.1 and standard deviation 1.7. Find the upper limit of the 95% confidence interval for the mean difference.

n = 9d̄ = 5.1sd = 1.795%t(8) = 2.306
upper limit = mmHg
4.Medium
n = 13, sd​ = 6.90LUd̄ = 3.8E = ?95%

The blood pressure of 13 patients is measured before and after a treatment. The differences d = before − after (mmHg) have mean 3.8 and standard deviation 6.9. Find the margin of error E of the 95% confidence interval for the mean difference.

n = 13d̄ = 3.8sd = 6.995%t(12) = 2.179
E = mmHg
5.Hard
p = 0.5, n = ?p̂ − Ep̂ + Ep̂E = 0.0299%

Nothing is known in advance about the proportion of defective products. How many products n must be inspected so that a 99% confidence interval for the proportion has a margin of error of at most 0.02?

p = 0.5E = 0.0299%
n =
6.Hard
σ = 18, n = ?x̄ − Ex̄ + Ex̄E = 295%

The population standard deviation is 18. 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 = 18E = 295%
n =

Answer key

  1. 1. W = 10.85
  2. 2. σ = 15.98
  3. 3. upper limit = 6.407 mmHg
  4. 4. E = 4.17 mmHg
  5. 5. n = 4148
  6. 6. n = 312

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