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 = 50, σ = 30L = ?Ux̄ = 53.5E99%

A sample of 50 measurements has mean 53.5. The population standard deviation is known to be 30. Find the lower limit of the 99% confidence interval for the mean.

n = 50x̄ = 53.5σ = 3099%
lower limit =
2.Easy
120.7x̄140.395%

A 95% confidence interval for a mean, computed from 25 observations with a known population standard deviation, is [120.7, 140.3]. What standard deviation σ was used?

[120.7, 140.3]n = 2595%
σ =
3.Medium
n = 13, sd​ = 1.60L = ?Ud̄ = −2.3E95%

The blood pressure of 13 patients is measured before and after a treatment. The differences d = before − after (mmHg) have mean −2.3 and standard deviation 1.6. Find the lower limit of the 95% confidence interval for the mean difference.

n = 13d̄ = −2.3sd = 1.695%t(12) = 2.179
lower limit = mmHg
4.Medium
n = 6, sd​ = 2.20LUd̄ = −5.4E = ?99%

The blood pressure of 6 patients is measured before and after a treatment. The differences d = before − after (mmHg) have mean −5.4 and standard deviation 2.2. Find the margin of error E of the 99% confidence interval for the mean difference.

n = 6d̄ = −5.4sd = 2.299%t(5) = 4.032
E = mmHg
5.Hard
p = 0.5, n = ?p̂ − Ep̂ + Ep̂E = 0.0590%

Nothing is known in advance about the proportion of defective products. 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 = 0.5E = 0.0590%
n =
6.Hard
σ = 14, n = ?x̄ − Ex̄ + Ex̄E = 1.595%

The population standard deviation is 14. 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 1.5?

σ = 14E = 1.595%
n =

Answer key

  1. 1. lower limit = 42.57
  2. 2. σ = 25
  3. 3. lower limit = −3.267 mmHg
  4. 4. E = 3.621 mmHg
  5. 5. n = 271
  6. 6. n = 335

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